-Try to change the charging cable or adapter, if can solve the problem, that's the reason of broken cable or adapter. -Try the magnetic charging. If can charge the phone well, the problem may be caused by wrong USB port. If can't charge either, your battery may be broken and need a replacement. - If new battery can't save your phone, you need take it to check the motherboard.
You can use the hair dryer to heat directly. You also need such tools as suction cup and several guitar picks or something else can help to cut the tape.