Chosen Solution

I’ve tried two replacement batteries. The batteries fit and screws in ok, but, the contacts on both [including an ifixit] replacements are slightly different and don’t make contact.

there is a iphone 4 , iphone 4 (CDMA) and iphone 4S. the iphone 4/4(cdma) have the same battery and the iphone 4s has its own battery. make sure you have the right battery for the device you are working on.