i had this problem, I went out into town on the weekend, I ende dup quatting for a wee and it had dropped from my lap which was only 309cm off the floor.
It wouldn't turn on, yet I knew I had around 50% so I called it a night and got picked up. Thinking I was a little bit too drunk I thought id put it on charge in case it was actually dead..
It turned on once I put it on charge! I could not tell you how happy I was with it! but then I realised my phone was saying 100% then I knew there was something wrong, I took it off charge and it turned off this did my head in!
I pressed really hard on my battery so it could fit back in place and surprisingly this had worked my phone was freely working off charge! I was very happy! until today. it fell off my lap and down the side of my seat in my car, (which isn't far down) and now It wont work unless charging, iv tried pressing down on my battery and it works for about 5 minutes and then switches off again! :l APPLE NEED TO SORT THIS OUT! but yeah if anyone else having the same problem just try and put pressure on the battery and push it down as hard as you can so it fits back in place. Hope this helps:)