Refrigerator runs on A/C but not LP

Mine had the same symptom last fall. The burner orifice was plugged so I took it off and blasted it with carb cleaner and all was good.

At least some Dometic fridge burner assemblies have a manual gas shut-off valve at the gas solenoid assembly. It looks like a large set screw, not so much like an obvious valve, and turns a quarter-turn from on to off or vice-versa. (It may be behind a sheet metal shield around the burner area.) If this is closed, opening it will certainly not hurt the situation. This is hardly the only thing that can cause non-operation on gas, but it is an easy one to check and fix if needed.

Here's a random picture from the internet showing the assembly (with various covers removed); the shut-off valve is just underneath the orange rectangular solenoid gizmo. (It's the one with the slotted head on the left, not the inset hex key one on the right.)

Is gas actually getting to the fridge?