I also had the same problem but with my lock button not working for months now. Last night my screen went completely black & any of the buttons are working.
Most of the suggestions I saw was press the lock&home button at the same time for 10-15 seconds, and it worked for some people but mine didn't (because of my broken lock button).
What I suggest is to completely drain your battery ( I left mine to drain for 11 hours) and what you do next is you plug the charger in your computer, if the low battery sign showed then ur saved. Now u just have to wait for the apple logo :)