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 :)
I had the same problem. What happened is last night i was about to sleep i checked my phone and any of the buttons aren't working, of course i went to search how to fix it and most of the suggestions are pressing the lock & home button at the same time for 10-15 seconds but mine didn't work considering i have a broken lock button for months now. and I went to search again and see i wasn't the only one so i felt relieved a bit. I've read everyone's suggestions here but I did one strategy that worked 100%. What you should do is completely drain your battery (I left mine to drain for 11 hours) and after that you should charge it in the computer and wait. If the low battery sign turned on then u should wait for the apple logo then ur saved.