Charlie this may be a long shot, but let me explain how I resurrected my fridge when it died. I tried everything to make it work, but no sale on that deal. It lit, the burner, 12V was fine etc but no cooling.
I was FT for 2 Alberta winters and it was really cold out. The fridge died exhibiting the symptoms you describe.
I bought a small bar fridge to hold me over until I could replace / repair my unit in the spring.
I removed the fridge from the TT and took it outside to the parking lot of where I was set up. I then "took it for a walk"
From the upright position, I laid it over on its side, waited I think about 30 seconds, may have been longer, a minute or 2, don't recall for sure. Then I turned it upside down and let it sit a for the same amount of time. Then on its side again, then back upright and so on, waiting in between flipping it. I repeated this process about 20 times or so (20 complete cycles from upright to upright), finishing with it in the upright position. I gave it about 15 minutes, then reinstalled it. I then waited for quite a number of hours, it may have been overnight, again, don't recall for sure.
After the wait was over, I turned it back on and voila!! Success!!
The fridge not only resumed operation, but worked 100% like a champ for the next few years until I sold it! It was I believe the spring of 2015 when I did that, and I sold the unit last fall, the fridge still working perfectly.
I figure a chunk of something internal came loose and blocked a pipe, and "taking it for a walk" dislodged it.
It's worth a try before you spend a gob of money and a bunch of effort on a new cooling unit or replacement fridge. What have you got to lose?
Mine was a 1997 model Dometic.
**On edit, I think it was maybe only about 10 times that I rolled it over, not 20. and I think I left it for at least a couple minutes in each position. Seems to me it took about an hour once the fridge was out. It has been a while, I forget exactly**