Well it is obvious you have DC cause the 'check' light is working
DC is needed for display, interior light, controls and propane function
(10.5V DC---13.5V DC to function)
AC is strictly for the electric heater element
If you have AC power source available check that the outlet fridge is plugged into works (plug a lamp, drill ect OR Voltmeter/RVs Friend)
In 'Auto' fridge will operate on 120V AC (priority source) and swap to 'gas' if AC Power is not available
'Check' light cmes on when the propane flame doesn't light off OR doesn't prove it light
Common issue when propane is valved out for extended period and then valved back in
A demand has to be placed on LP Regulator to establish flow.....fridge burner is a small demand
Lighting off stove top burners (all on high) will place a controlled demand on LP Reg and establish the flow of propane into system
Then several attempts of lighting propane burner off maybe necessary to get flow to fridge burner
THEN it will take 8-12 hours for freezer and THEN food compartment to finally cool down enough to use (safe food compartment temp of 40*F and below)
Fridge looks like a Dometic Americana