Battery not recognised after overheating

I have a MBP mid 2012. I was doing a batch of converting video files to a smaller size using handbrake, and left it on charge. When I came back, the magsafe was showing green so I unplugged it, and the computer immediately switched off.

I reattached the power cord, and the machine switched on, but the lights on the battery checker were flashing when I pressed it, and the internal clock had reset. Removing the power cord shuts the computer down immediately.

Initially I thought that it might have just been something that a new battery would fix, but having looked at coconut battery it says that the battery is still fine. The OSX system profile does say replace now, but that it still holds charge. I've tried doing the PRAM and SMC reset.

My question is - is this a battery problem or something on the logic board, or something else entirely?