Computer shuts down randomly on battery power
I have a Macbook (Mid-2009, non-unibody, NVIDIA 9400M) that is randomly shutting down. When the computer is plugged into the power adapter, it will work perfectly fine and not exhibit any problems. However, if I unplug the computer and work solely on battery power, the computer will randomly shut down without any warning. In order to turn the computer back on, I will need to press the power button. The battery is new and has 2 cycles on it - I have swapped another known good battery from another Macbook and the problem still exists.
A search on the console log shows that the computer has previous shutdown causes 3 or 0.
Also, I opened up the computer to visually inspect the logic board and saw that there is nothing plugged into the J5520 (TEMP) socket - could this be the source of the problem? I'll attach a picture:
Thanks in advance for any help.