The 110 volt side of the fridge is just a thermostat and heater. Find the 2 wires for 110v that go into the heater, disconnect them, and put 110v directly onto the leads to the heater. Wait a half hour and check the freezer. If it's cold, then the basic cooling system is working and you have a thermostat problem. If the freezer doesn't get cold, check the heater stack to see if it is warm. If cold, then the heater element is bad.
BTW: I was able to find product and service manuals on the web for my Dometic.