I also had this problem, except I noticed one thing: When I tried to call my phone, it would ring, which meant the battery isn't dead, just in a seriously bad state. To fix it I just left it for about 15 hours (I got lucky it didn't have much battery left) until it actually died, confirmed it was dead by trying to call it, and then plugged it into the wall to charge it, at which point it turned on.
This problem sucked especially for me because I have a broken lock button, which meant there was no chance of holding lock and home to reset the phone.
Hope this helps.