its obviouse that the battery of the controller powers the motherboard. Btw, it can happen if the contoller of the playstation 3 has took some damage. if it is turning on and not connecting u can play it by connecting the charger to the playstation and the controller, in a while it would be connected, if it is not even turnings onn its usually a wire problem, so u can check if any wire or anything inside is damage and reply back. Thank you :)