Dometic fridge not cooling

I have a 2000 Sunnybrook 5th wheel that has a Dometic model RM 3662 refrigerator in it. I leave it plugged in continuously while it is parked in my yard. I went out to get something today and found that the fridge was not working. All of the lights are on and all looks ok. I took off the outside panel and did not smell ammonia or see any yellow stains from an ammonia leak like I saw in my friend’s RV when his sprung a coil leak. Also the coils were not warm.

I have never used it on propane so I cannot say that it works when using propane. I unplugged it from the A/C outlet and could hear the ticking of the propane igniter attempting to light the burner. When I plugged it back into the A/C the unit clicked like it was turning on.

With the ticking and clicking, it leads me to believe that the circuit boards are ok. Of course I may be wrong. Since I did not smell or see any ammonia signs it leads me to think that the heating coil may have burned out from leaving it on all the time.

We changed out my friends coils last year and it was a very easy job. He is coming over tomorrow and we will pull it out of the wall and inspect it. I think I will try it on propane before we pull it.

Any suggestions before we get started?

Thanks in advance for any suggestions.