The Dometic fridge in my 2005 FF works great when I run off LP, but for quite some time now, it doesn't seem to work at all on electric. Is there a separate thermostat or fuse for the electric portion of the fridge?
My 2005 T160 FunFinder has only one thermostat that operates both 120 volt and LP. It appears you are not getting 120 volt power to the fridge so the first thing to check are the breakers to ensure one isn't tripped. It is possible the 120 volt stack heater is burned out but more likely somehow the stack heater isn't getting power. It is possible the 120 volt side of the thermostat is defective and the side that controls the gas valve is ok.
Based on the details you have provided, it is very possible to have that in your fridge. But as one has said, you have to check first the volts so that the ref can run. It will help you determine the problem.