Big Bang 2.0 was supposed to restore the universe using atoms from the original universe which had been preserved inside the Pandorica before the TARDIS blew up (by transporting the Pandorica into the heart of the TARDIS explosion, they would provide its 'restoration field' with so much energy that it could use the information contained in these atoms to restore the whole universe as it was--see "Update" below for quotes on this). From the transcript of "The Big Bang":
DOCTOR: How can that Dalek even exist? It was erased from time and
then it came back. How?
RORY: You said the light from the Pandorica-
DOCTOR: It's not a light, it's a restoration field. But never mind,
call it a light. That light brought Amy back, restored her, but how
could it bring back a Dalek when the Daleks have never existed?
AMY: Okay, tell us.
DOCTOR: When the Tardis blew up, it caused a total event collapse. A
time explosion. And that explosion blasted every atom in every moment
of the universe. Except-
AMY: Except inside the Pandorica.
DOCTOR: The perfect prison. And inside it, perfectly preserved, a
few billion atoms of the universe as it was. In theory, you could
extrapolate the whole universe from a single one of them, like, like
cloning a body from a single cell. And we've got the bumper family
I don't think it's entirely clear, but my guess would be that the Pandorica would only restore the universe to the state it was in at the moment the Pandorica had been sealed up (using things like minute dust particles or air molecules which had gotten inside along with the Doctor at the time, perhaps, or maybe even the atoms the Pandorica itself was made out of), in the previous episode "The Pandorica Opens". And in that episode the cracks had already erased Amy's parents, so without Amy using her special ability to fight against the memory-erasure caused by the cracks (due somehow to having lived in the room with the crack in the wall), it would just restore a universe where she had no parents.
Also see this answer to a related question, which speculates about how the cracks don't completely write people out of history, but instead leave some traces of their lives even though most people don't consciously remember them (though time travelers can be an exception to this, as established in 'Flesh and Stone' when Amy asks the Doctor how she can remember soldiers who were erased by the cracks).
Update: For reference, since you asked about this in the comments, here are some additional lines backing up the idea that the point of transporting the Pandorica into the exploding TARDIS was to provide energy to its restoration field--the "light" which had revived the Dalek, as Rory termed it in the earlier quote--so it could reboot the universe using the "memory" contained in the atoms inside it:
DOCTOR: The box contains a memory of the universe, and the light
transmits the memory, and that's how we're going to do it.
AMY: Do what?
DOCTOR: Relight the fire. Reboot the universe. Come on!
RIVER: Doctor, you're being completely ridiculous. The Pandorica partially
restored one Dalek. If it can't even reboot a single life form
properly, how's it reboot the whole of reality?
DOCTOR: What if we give it a moment of infinite power? What if we can
transmit the light from the Pandorica to every particle of space and
RIVER: Well, that would be lovely, dear, but we can't, because it's
completely impossible. DOCTOR: Ah no, you see, it's not. It's almost
completely impossible. One spark is all we need.
RIVER: For what?
DOCTOR: Big Bang Two! Now listen.
The Doctor then gets shot by the Dalek, but when they later find him alive and well, River continues his thought:
RIVER: The Tardis is still burning. It's exploding at every point in
history. If you threw the Pandorica into the explosion, right into the
heart of the fire.
AMY: Then what?
RIVER: Then let there be light. The light from the Pandorica would
explode everywhere at once, just like he said.
AMY: That would work? That would bring everything back?
RIVER: A restoration field powered by an exploding Tardis, happening
at every moment in history. Oh, that's brilliant. It might even work.
He's wired the vortex manipulator to the rest of the box.
RIVER: So he can take it with him. He's going to fly the Pandorica
into the heart of the explosion.