Iphone would turn on and off.

I'm really upset about this whole iPhone deal. About a week ago I dropped my iPhone on the wooden floor. (it's also dissapointing to say but the iphone had an otter box if it is a hardware problem. I thought they were made to protect it from things like this). That night I started experiencing the iPhone turning off and on by itself. It would turn on for about 3 minutes, and then cut itself off. I assumed that this was just a low battery or something so I left it on the charger. I came back a while later to realize that even on charge, the phone was rebooting itself over and over. It wouldn't even charge. The battery would steadily get lower until the 3G and wifi failed. I turned off the iPhone the next time it rebooted so that it could charge somewhat. When I turned it on the next day it had a full battery, until it cut itself off again. Then it read about 45% battery, and steadily went down as it kept on rebooting. So I decided that maybe if I could update it, that it might fix it. Dumbest idea I've had for a long time. The iPhone cut itself during the update. Now itunes is giving me messages that the Iphone must be restored, but when I try to, the phone cuts off before it can complete a restore. Any suggestions on what I should do before I go to the apple store and ask if I need to buy a new phone?