I agree with bcastner:
I just got done with a cell phone that worked fine on the charger, but was dead on (good) battery . On dis-assembly, I found that the edge contacts on the charging port were cracked. When the charger was plugged in, it would "align" the board and it functioned OK. When the charger was removed, the pieces would slip and short out the phone. Can you check the charging assemnly? You might have a similar situation. (Just backwards).