I replaced the screen and back on a Verizon iPhone 4 for someone, afterwards it worked fine for me. After about a day, it started to act up and shut off and not connect to the network (Verizon). Here is what I see looking at it again, will not power on, not low battery, If I unhook the battery and plug in the charger it will power on, but will not connect to Verizon and shows 100% battery, when I plug the battery back in it shuts off immediately.

I believe the battery is shot, but not sure what else to say is the issue, has anyone seen a similar issue or know what the cause could be? Thanks.