Hi @funghoul
Not sure if the following is totally applicable but maybe worth a look.
Here's the [document|27709|mini manual] for a GE ''***GFE26 series*** refrigerator''.
It is not the exact manual for your model as that is GE publication 31-51982 (can't find that one) and the above is GE publication 31-51901 but hopefully it is close enough to still be of some help.
The manual shows how to get into the service mode so that any fault codes that are being stored will be displayed. It also describes how to individually test all of the functions to make sure that they're OK as well.
Hopefully this may be of some help.