How to get my contact and pics out of my broken iphone 4?

My iphone 4 is broke so I got a new one, now I need my contacts but I can't get them due to the fact that the phone doesn't want to turn on. I think the battery died. I don't have my contacts on my icloud so that solution is out of the picture what the best way to get this fixed maybe the apple store can help me or am I gonna need to buy another battery just so I can turn it on to get my contacts and pics

Well you can't take the battery out yourself so you have to bring it to an apple store anyway. But once you have the new battery in there youll have 2 good phones so if i were you id sell one