Author's Note: This exploit is of dubious canonicity. If a corporeal Patronus is solid, it works. If not... AU, I suppose?
"Hermione," Harry said suddenly, looking up from the books they were studying. She looked back at him with tired eyes; even she could only take so much nonstop cramming. As for him, this was more studying than he'd done during his entire time at Hogwarts, but if it was a choice between that and certain death... "The Patronus Charm. I control it, don't I?"
"I believe it says so on p. 357 of Wilkes & Fawley... or was that p. 234 of Greengrass & Shafiq? That section of Wilkes & Fawley was about Lethifolds, I think, but not the Patronus Charm specifically. Oh, I don't even know anymore..." Her eyes filled with tears.
"The point is, I control it," he said hastily, uncertain whether he should pat her on the back. "And it's solid, I'm pretty sure - it knocked Malfoy and his lot over back in third year, and it drives back Dementors pretty well."
She looked at him blearily, wiping away her initial tears. "And? Harry, I don't... You can't know you'll be facing Dementors."
"It's solid," he said in a slow, calm voice. It wasn't her fault - he'd caught the traditional nap in History of Magic and she, for whatever insane reason, actually paid attention to Binns. Apparently the minutiae of goblin troop movements were quite interesting once you really immersed yourself in the subject. "I can control it - I must, since Aloysius Abbott developed a 'highly advanced' method of sending long-distance secure messages with it. That requires, at minimum, the capacity to take basic commands and act upon them. Otherwise, where would it know where it was going?"
She squinted at him, but comprehension was beginning to dawn.
"It's a remote-controlled magical construct," he finished. "If I can learn how to command it - and I don't need the part about making it speak aloud, that's supposedly the hard part - I can have it carry out tasks for me at a distance. Which means..."
"But Harry, you've only got two more weeks," she said, eyes widening. "Can you - do it in time?"
He shrugged. "Nothing so concentrates the mind as the sight of the gallows."
Harry's entrance into the arena was met with hushed anticipation, then gasps of astonishment as he summoned a full-fledged stag corporeal Patronus for all to see, and then... booing as the stag sprinted straight for the golden egg and knocked it out of the nest. Unfortunately the stag was soon met with dragonfire.
Fortunately for Harry and unfortunately for the audience's taste for bloodsport, he had enough stamina to keep resummoning the Patronus and instructing it to knock the egg further away from the nest, until the egg was at last far enough away for the dragon to not be able to cover both it and the nest at once - at which point the stag's latest iteration was sent to harass the nest, distracting the dragon long enough for Harry to creep over and retrieve the egg.
The judges were torn between scoring him well for proficient use of an extremely advanced and powerful spell and docking him for a boring and repetitive way of handling the problem. Harry couldn't have cared less. He preferred not being carbonized.
As soon as the judges announced the start of the Second Task, Harry knew immediately what to do. Standing at the edge of the lake, he drew his wand, shouted "Expecto Patronum!", and commanded the Patronus to go down and retrieve his hostage. It leapt into the lake and plunged downwards, its glow faintly visible below the surface before it dimmed out of sight.
Then it reemerged without his hostage, shaking its head before dissipating. He bit his lip, wondering where he had gone wrong, and then realized the likeliest explanation.
Thus the next Patronus was commanded to go down, loosen any bonds preventing retrieval, and then retrieve the hostage. It dove into the lake, and shortly reemerged, having managed to somehow maneuver Hermione onto its back, and swam to Harry before dissipating. He pulled Hermione out of the water, grinning broadly, and hugged her semi-conscious form before turning to the judges.
They all wore very odd expressions. Harry looked at them curiously; they avoided his gaze.
At last, Karkaroff cleared his throat and spoke up. "An excellent job retrieving Viktor's hostage, Potter," he said dryly. "Now, would you mind retrieving your own?"
Harry looked at Hermione, now groaning and stirring in his arms, and then at the judges. "What are you talking about?" he asked. "Hermione was mine. She must've been - I know she's Krum's girlfriend, but we've been friends much longer than that - she's the one I'd miss the most." Madame Maxime sighed dramatically, pressing a hand to her chest, and muttered something under her breath that he couldn't quite catch, but it seemed to annoy the other judges. "Who else would it be?"
The judges looked very uncomfortable again. "Mr. Potter..." Dumbledore said eventually. "Did you not notice Mr. Weasley was missing this morning?"
Harry blinked. "Oh, I just figured he was being a prat and avoiding me again."
Bagman's wording for the Third Task was that "the first Champion to touch it will receive full marks". They didn't, technically, say the Champion in question ever had to go into the maze.
After commanding his Patronus to go into the maze, retrieve the Cup at the center, and avoid any other humans on its way in or out, he leaned back against the hedges and grinned at the long-suffering judges. "You ought to go into the maze, Potter," Moody said gruffly as he passed the boy in his patrol around the hedges. "No guarantee something in there won't be able to wreck even your Patronus."
"Yeah, but if it can wreck a powerful magical construct, won't it be able to wreck me?" Harry said brightly. Moody glowered at him and opened his mouth to speak -
"Moody," Karkaroff said with false sweetness, "as a judge, I must note that it is against Tournament rules for a Champion to receive external help during a Task, and I simply must disqualify Mr. Potter on the spot if you continue."
Moody turned and gave Karkaroff a look of absolute hatred, then turned back and lumbered past Harry. "You know," Harry commented to the general audience, "it doesn't matter too much to me about winning - I tell you, I did not put my name in the Goblet, nor did I have anyone do it for me. I did the First Task because I didn't want to die, and the Second because I didn't want - the one I'd miss the most to die." Madame Maxime beamed at him; she had inexplicably given him full marks on that Task even before he brought up his actual hostage, announcing she was doing it more for "higher principles" than his actual actions... Whatever that meant. "This one? Well, I suppose it's nice if I win. But I'm not going to die if I don't go into the maze myself, am I? I am making my best effort to win this - considering what my best spell is."
"Mr. Potter, now is not the time to pontifi-" Dumbledore began, but Harry cut him off.
"Great, I'll make it short, then. How's 'I'm not eleven or twelve any more, and I don't think a nice shiny trophy's enough reason to risk my life against horrific monsters because your security's absolute rubbish, sir'?"
"What does 'e mean by zat?" Madame Maxime asked, peering at Dumbledore, who was wearing an uncharacteristic grimace. He did not reply.
Some time later, the Patronus came galloping out of the maze, the Triwizard Cup dangling off an antler. Harry brightened as he saw it. "Well, that's that, then," he announced, reaching for it. "I'd like to thank Mr. Remus Lupin for personally tutoring me in the Patronus Ch-"
When faced with an unfamiliar situation, Harry opened with his Patronus. He ordered it to guard him, then started walking towards the exit to the graveyard. Doubtless this was some silly unannounced Fourth Task and he was supposed to complete some trial symbolic of death. Well, to blazes with that - he was just going to find his way back to Hogwarts, pretend he didn't know what was going on, and force the judges to explain the new Task to him before he did anything. They might as well suffer a bit too...
By the glow of the Patronus circling him, he saw a figure approaching him, a bundle cradled in his arms. "Hello?" he called cautiously as the figure halted. "Could you at least explain to me what this is all ab-"
A sudden bolt of pain hit him between the eyes. As he staggered, blinded by the agony piercing his skull, he heard a voice begin a spell -
That was drowned out by his own scream of "CHARGE!"
His Patronus obeyed, and he did not need sight to know the collision of a man with a stag's antlers was an ugly thing. As he dropped to the ground, supporting himself on his hands and knees, he managed to force his eyes open; as his Patronus charged off into the night, he glimpsed a crumpled, unmoving form. "Get up! Get up, you fool!" he heard a voice hiss, and something familiar about it convinced his legs to work again despite the pain.
As he stumbled to his feet, he called the glowing stag back; with an effort of will, he made it return to him, and leaned on it for support. He did not think he could renew it in a timely manner, not when his head hurt this badly...
"Never mind... never mind... KILL POTTER!"
He froze, understanding the order, but not understanding whom it addressed, or where -
OH GOD, THAT WAS A BLOODY HUGE SNAKE!
With a scream, he leapt away from the plunging fangs and staggered away, then set his Patronus upon it as the snake reared again. With stag and snake locked in mortal combat, he whirled towards the graveyard exit and ran for dear life. A pox on the bloody Tournament! He hadn't even wanted to be in the ruddy thing anyway!
The Tournament proper ended an hour later, when the judges finally jury-rigged a way to use Hogwarts' auto-addressing abilities to discover Harry Potter's current location, and found him in a minor and seemingly random village a few hundred miles away. Fudge dispatched Aurors to pick him up immediately; they found the boy disoriented and exhausted on the road leading out of the village, having incoherently decided to hike to London. Upon questioning, he babbled something about an attacker in the graveyard and a giant snake.
The Aurors sent to check the graveyard discovered the boy's Patronus still battling a gargantuan snake, one that proved resistant to multiple spells, and called for backup. After subduing the snake (at which point the Patronus immediately dissipated), they discovered a dead man with the Dark Mark lying on the ground, his torso bearing the marks of extreme trauma, accompanied by a disturbingly infant-like homunculus attempting to crawl away from the corpse. It hadn't made it very far. All were taken into custody as evidence, with particular attention being paid to the dead man: they'd finally found the rest of Peter Pettigrew's body, but thirteen years overdue.
A bemused Dawson Dawlish found himself at Hogwarts, still holding the Cup he'd absently picked off the ground, and explained the situation to the judges and audience. It did not inspire further confidence in Dumbledore's "absolute rubbish" security. The situation worsened when he greeted his old colleague Moody, with whom he had an old rapport, and found that the man did not recognize him; upon further questioning, the man suddenly turned violent, had to be subdued, and was discovered not to be Moody at all. In fact, much like Pettigrew, he was both Marked and supposed to be long dead.
Since all this happened before a massive audience, even the Ministry couldn't cover it up.
The boy, meanwhile, was suffering from more than mere magical exhaustion. Due to his disorientation and complaints of constant headache with developing hallucinations (of the Aurors who had gone to the graveyard, coincidentally), the Aurors elected to override their orders to immediately return him to Hogwarts in favor of hauling him straight to St. Mungo's. There he was examined, examined again by a specialist, examined again by a second specialist, examined again by a member of the Department of Mysteries, and recommended for surgery as soon as possible. As his condition was deemed not imminently life-threatening, he was permitted to travel by Portkey to Hogwarts, be quickly declared the official winner of the Triwizard Tournament, and return immediately to St. Mungo's for surgery. After a marathon surgery, he was held for seven days before being released with a clean bill of health.
Officially he had a brain tumor removed, which was mercifully caught before it advanced. Unofficially he had a brain tumor removed, which was mercifully caught before it advanced. It was just of a rather singular sort.
Meanwhile, the Sirius Black case was reopened due to Peter Pettigrew's extremely belated demise, and the Department of Mysteries started scouting around Britain as part of a mission whose details were classified. The Quibbler claimed that Voldemort suffered from multiple personality disorder, causing the emergence of several ghosts upon his death whom the Ministry was now forced to exorcise; this was of course absolutely absurd and absolutely unrelated to the editor's encounter with several intimidating wizards in grey cloaks within twenty-four hours of the article's publication.
The young Champion himself had a long and interesting conversation with Madame Maxime after he was released from St. Mungo's, and thereafter both he and a certain female friend submitted transfer applications to Beauxbatons.
Author's Note: It's a truly peculiar feature of the books that Harry learns his most advanced spell in third year.
Now to return to the crucial question:
Is a corporeal Patronus solid?
On the one hand, Merriam-Webster defines "corporeal" as "having, consisting of, or relating to a physical material body". Collins defines it as " of, for, or having the nature of, the body; physical; bodily; not spiritual" or "of a material nature; perceptible by the senses; tangible".
On the other hand, if it were solid, wouldn't it be used offensively against non-Dementor foes more often? However, perhaps intent concentration on a single happy memory is a bit hard in combat against foes who have more attacks than "be depressing" and "worst snog ever", or perhaps the incantation is too long to usefully deploy in a high-speed duel... in which case it should have still made a showing during large-scale fights like the Battle of Hogwarts.
Then again... JKR's logic regarding Patronuses is inscrutable, since I can't figure out the connection between "guardian spirit summoned by happy memories" and "magical text-messaging system" for the life of me, yet she seems to regard it as a natural and obvious thing...