I've worked on my 10 plus year old GE Fridge alot.
I've been through 2 Main Boards. Takes about 15 minutes to change one. You can guilt GE into selling you one cheaper, or get a knockoff from AMAZON. I've also change a thermister or two.
Lots of YOU TUBE videos on troubleshooting fridges.
Just type in what its doing and the brand and you will be amazed what comes up. Most of the online parts places have pretty good trouble shooting guides too, with the resistances for the pin outs for good / bad.
There isn't much to them, and so far in my experience I've not seen a compressor or mechanical go - its always been a sensor or a board - so easy to fix myself.
If you have a volt / ohm meter pretty easy to diagnose mostly on your own, and get it down to where you are only throwing a couple of parts at it - as long as you are sure the mechanicals aren't dead.