My iPhone 4 won't work unless it's connected to power?

My iPhone 4 fell off the counter, and now it won't turn on unless it's connected to power. When I disconnect it, it immediately turns off. It is also stuck at 68% battery and won't charge from there when it's connected, it just merely stays on. What's going on? What can I do?

Very probably the impact distorted the battery terminals so that it isn't making contact any more.