Asus G551JM keeps shutting off once the charger is removed.

Hi everyone, I'm new here. I have been searching endlessly for a solution to this problem to no avail. My Asus G551 started shutting off about a year ago while on battery even though the battery still had power. Initial I thought it was the battery (which did eventually go bad and was no longer charging at all) so I've bought a new battery and a new charger (to be safe). I charged up the battery when I got it to 100% and then used it on battery until at about 54% when the laptop again just shut off without warning. Now, it will only work on the charger and once the charger is removed, the laptop will completely shut off as if it has lost all power even though the battery has power and is connected. I've not used it as I'm afraid I'll mess up the new battery. The laptop is no longer on warranty so there's not been much help from ASUS. Does anyone know how to solve this issue?