Vergil didn't look like he 'died', especially compared to the rest of the higher demons defeated by Dante. Capcom states that he still holds a big part of the DMC universe, so it's hard to argue about him being alive, since they confirmed him to appear in DMC4, though nothing further than that has been explained.. Thing with Vergil is...well, you see, when defeat 100 enemies in the Credits roll during the end of DMC3, you'll see a special cutscene in which Vergil plummets to Hell, and tries to take on Mundus, who was there at the time. However, Vergil was weakened from his battle with Dante and lost, and was subsquently brainwashed. However, I cannot say he was completely corrupted, since his honor was still intact and the way he reacted to seeing Dante's half of the Perfect Amulet