Refrigerator is dead

We have a 2009 Casita trailer with original Dometic fridge. We're full-timers and typically boondock so the fridge uses propane and 12V. Today, out of nowhere, the fridge went dead. The "ON/OFF" button doesn't do a thing. I figure it may be time for a new fridge looking at the age, but, as these things usually break in the worst possible location, I'd like to see if I can get it going again as we're currently in the middle-of-nowhere Alaska for the summer and are not going back to the lower 48 until the end of September and there's no RV repair shop in hundreds of miles here.

Anyone have any troubleshooting steps I can try? I already checked the 15AMP fuse and it's good (that would have been too easy a fix!).

Thanks!