Dropped iPhone can Cause damage to the battery??

Today I dropped my iphone (not in water, and it was inside of a case) and it wasn't turning on or anything. I got home and connected to my computer (via usb) and still no response. I connected to my wall charger and voia-la an apple logo. about 5 - 10 seconds after the logo appears the phone turns back off. So I connected my wall charger to my dock and sat my phone on the dock and the phone repeatedly turns on for 5-10 seconds and powers off. I'm convinced that when I dropped my phone it damaged my battery but am not sure. If this is the case would apple cover this under warranty?