The first thing I did was get a digital photo of the ID plate. Super helpful when looking up parts. The problem that my Dometic was experiencing was when I tried to switch to propane mode the unit would fault. (red light flashing). All other modes worked fine.
The second thing I did was read forums until I had read about every other person who had ever had problems with this model of fridge and whether or not they ever fixed their problem. Most of these folks found the weak link to be the main control board in the rear of the unit. Since I had no way of testing my board, I chose to upgrade anyway to a USA made Dinosaur Electronics P-246 plus which is said to be much more reliable. Also, since the 12 volt and the 120 ac modes still worked flawlessly I knew the cooling unit was not to blame.
When you're using ebay, always do your own research and query the exact part#. I've saved hundreds on parts by this trick alone. RV dealers want your money. I repeat, RV dealers want your money. Skip the middle man and find the direct part supply. I was not able to find a direct source for the main board but I did find a least expensive alternative. $155
After replacing the main board with no change in behavior, I was left with the re-ignitor board (above)
Dometic Part#2931132019 $33 Shipped! This unit is $100 or more if you search without the part#.
It took 5 minutes to install last night and zap zap zap, I was in propane refer heaven. This clean blue flame is what you're looking for during burner inspection.
Now I have the old main board (good for a backup) and I ordered 2 re-ignitor boards (one for backup) and my Dometic RM 3804 is essentially electronically new for less then $200