I have a similar GE side-by-side. The freezer wasn't cold enough because the damper that lets cold air into the fresh food side was stuck open. The fresh food thermistor was to blame.
I learned a lot about the inner workings from the Technical Service Guide (including how to get into the diagnostics.)
I found this link for you:
https://www.frontloadbearings.com/ge-profile-side-by-side-refrigerator-service-manual/#.ZCxSNHbMLIU
It shows the mini manual is inside the control console atop the fresh food compartment.
You're right about the main board. I found this video which shows the most likely parts that go bad. I had a WR55X10942 board lying around that I had replaced years ago. Got it out, noticed 2 bulging capacitors, replaced them, and now have a working spare.
https://www.youtube.com/watch?v=E_HChSIIif8