The small fan visible from the access door on the street side is a cooling fan for the fridge exterior cooling fins. If the fins don't get hot, the fan won't come on.
The air conditioning is not related to the fridge. If you have a problem there it's not related to a fridge problem, unless you don't have 12 VDC inside the AS.
The converter should be providing 12 VDC inside the AS. If you can turn on the ceiling lights then the converter is putting out voltage.
If the fridge is not cooling on propane or shore power then you have a problem with the fridge. As suggested, look for a clip on the inside of the fridge cooling fins in the back. It should be clipped on the fins. I think higher is cooler and lower is warmer. If this hasn't helped then you'll need to visit a local service center.