All the symptoms point to a refrigeration system maxed out, that's why it is running all the time, new motherboard would not fix it.
For a fridg running all the time, the freezer should be colder. Also, depending on electric rates, you are probably wasting $100 per month.
I would try to replace the two fresh food thermistors, one located behind the damper cover, the other, ( if you have a second one) at the bottom of the fridg section, just might fix your problem. Stuck in ice water, they should each read 16.6 kohm.