Refrigerator motherboard mystery

My GE Profile side by side refrigerator has stopped working. The interior light works but nothing else. I made the assumption it was the motherboard and when I took off the access plate a strong odor of ozone was released. Also a a resistor on the motherboard looked like it had overheated.

I then installed a new motherboard but no joy. Just quiet clicking noises. I then checked my connections. That’s when it got interesting. When I removed the plug at J2 the LED lights started working, the water dispenser worked, and the compressor kicked on. When I plugged the J2 plug back in everything stopped again. If I leave the J2 plug unplugged, the compressor gets very hot and the fan never kicks on.

I have a multimeter but I’m not particularly handy with it nor do I know where to go to next in figuring out this problem. Hopefully with the symptoms I described above the cause of my problem will be fairly easy for someone to diagnose. Appreciate any and all help. We need to get our refrigerator back up and running and would like to avoid an expensive repair call. Thanks.