Dropped Iphone 4 and now it won't turn back on?

I got an iphone 4 for christmas and the other day it fell on the floor. Now it won't turn back on. It works when i plug it into the computer but when i unplug it, it only works for a minute then turns off and its fully charged.

You broke it when you dropped it.

Remove the battery and re-insert it… Work now?

if not, you broke the internals of the phone… If you have wireless insurance, get it replaced for $99.99… If you don't have wireless insurance, then congratulations---you now have a new paperweight…

or, a 3rd party cell phone repaid shop or Applestore could fix it. For $50-$75 parts and labor

Remove battery and maybe you broke it