SPOILERS! DO NOT READ IF YOU HAVE NOT READ ALL OF THE BOOKS!
Prologue: Differences between Sixth Year in HBP and Sixth Year as it happened before the events of this story...
(This is simply a point-by-point list to establish some background for this story. It does not represent in any way the writing style of the actual story :-D So check out Chapter 1 before you make any judgements!)
Draco was ordered to kill Dumbledore, but was never given the Dark Mark.
Snape never made an Unbreakable Vow to protect Draco and complete his mission should he fail, because Narcissa never asked. She wasn't allowed to leave Malfoy Manor.
Dumbledore was not dying, because he didn't make the mistake of touching the cursed ring.
When Dumbledore offered Draco and his parents sanctuary, Draco chose to accept the offer. When Snape showed up and learned how the situation had changed, he diverted the other Death Eaters with the lie that Dumbledore had managed to flee, at which point they all 'chased' him to the gates of Hogwarts (followed by a number of Order members) and, when realizing he had 'gotten away', were forced to leave Hogwarts and return to their master's side.
Snape therefore maintained his cover, was able to help Dumbledore recover from the green potion from the cave, and continues to serve as a spy. While Harry now knows Snape is on their side, as he was on the Astronomy Tower and so saw him divert the Death Eaters when he could just as easily have killed Dumbledore, Snape is also still a bastard to Harry and Harry still loathes Snape.
Voldemort was very displeased to learn that Draco had failed him and managed to avoid returning to him for punishment and, when he called for the elder Malfoys only to learn that they were suddenly missing as well, became quite determined to see the Malfoy line extinguished completely.
Since Dumbledore is still alive, he is also still the main person working on the 'Horcrux Problem', but that doesn't mean Harry has forgotten about them completely.