The cooling system is the same for LPG or electric.
Either system provides a heat source to pressurize the cooling solution in the pipes on the back of the refer.
If the fridge works on propane, the cooling system is working.
As mentioned above, check the simple things first. The 120 volt "heater" is simply an electric element. Make sure the 120 volt outlet has current. If so, the problem could be the element has failed, or a wiring problem, or a control circuit board problem.
All a pain, but not near as bad as a fridge that won't get cold at all.
Jeff & Cindy
'09 27FB Flying Cloud
'91 350 LE MH