OK, let’s give this a try, carefully disconnect the battery from the logic board, with nothing connected press and hold the power button for a good 15 secs to discharge the logic board. Now carefully plug in the MagSafe charger, your system should spontaneously start, let it finish and do a proper shutdown. Now reconned the battery and restart your system. Let it run a good 10 minutes off battery and take a fresh CoconutBattery snapshot, now plug in the MagSafe charger the system should start charging the battery again, take one more snapshot and post both here for us to see.