My iPhone battery won't work?

I have an iPhone 4.It sorta-kinda somehow fell down the stairs, the back plate fell off (it was already loose), and the battery fell out. Now, no matter how I put the battery back in, my phone won't turn on again. No pieces fell out during the fall, and I have been able to take the battery out and put it back in without any problems before.
Although, when I plug the iPhone into the charger or my computer, the apple logo that comes when you turn it on appears, but it stays that way for ages. It never turns completely on…

I have EVERYTHING on that phone. Pictures- important memories, notes, contacts, calendars…
Someone Please be an angel and help me, I NEED my iPhone back.

Have an iPhone tech look at it.

And you really think that a fall that caused the phone to fly apart wouldn't damage something else? Take it in for service.