spontaneous charging (or lack of charging)

So I have a white macbook. The logic board was bad-it was replaced, then the battery connector was also bad-that was replaced. Now the computer will run from battery IF the battery was charged in a different laptop. When plugged in it says its charging the battery(verrrryyy slowly) but the computer hibernates when i unplug the power cord. It runs fine when plugged in, but can't seem to charge the battery. Is this the fault of the battery? or the battery connector?