Periodic Shut Down/Not Turning On Troubleshooting

2009 Macbook Pro A1297 Emc 2329 2.8Ghz

Hello I'm working on this Macbook and since I'm a PC Guy I joined this community to learn more.

The Macbook is a A1297 EMC: 2329 2.8Ghz model running OS X 10.7.5. It came in because it would periodically turn itself off, and eventually would no longer turn on. As far as I know this Macbook has no other known issues. When I pressed the power button nothing happened; no fans, no HDD spin-up, no LED's, nothing. This happened whether the Macbook was plugged in or not. I pressed the battery indicator button and it showed it to be at 7/8 charge.

First thing I did was look up the specs to accurately troubleshoot. I then removed the back and tried to power on the Macbook by the two silver jumper pins on the logic board to no avail. When this did not work, I disconnected the battery and charger, pressed and held the power button for 10 seconds, reconnected the battery and pressed the power button. Boom, the Macbook began to power on, however; during the grey load screen it shut itself off again. I plugged in the charger, pressed the power button once more and it turned on and remained on. I have now unplugged the charger and continue to use it and it has not yet shut off.

To further troubleshoot this I turned it off and attempted to turn it back on with the charger out (battery now indicated to be at 6/8) and it does not turn on. It tries to spin-up but it then cuts off before the screen ever illuminates. I plugged it in and attempted to turn it on and it came right on.

EDIT: After reattaching the back panel I attempted to power on the macbook with the charger plugged in and it turned on, began to boot, gave me the signature apple chime and then shut off. It did this twice, before I got it to come on and stay on.

What does everyone believe to be the problem? I am leaning towards a bad battery even though it seems to be holding a charge, or perhaps something wrong with the logic board?