iPhone 5 Reboot Loop..?

A few nights ago, I was woken by the sound of my iPhone 5 hitting my carpet floor. In the morning I noticed that my phone wouldn't turn on, so I connects it to my charger. I was surprised when it the apple logo immediately appeared, then 3 seconds later it shut off. It came back on 3 seconds later, then shut back off. It only does this when on a charger. When not connected, it doesn't start at all. I have tried to restore it at least 15 times, getting different errors each time. (11,12, device not found, etc.) I would rather solve this at home instead of at a Genius Bar. At the moment, it is rebooting and shutting off and repeating.