Never used on gas, per OP, could mean dirty gas orifice or spider web in burner tube. Spiders do like the smell of LP.
Turn off the fridge for five minutes. Open the outside fridge cover for something to do during that time. With no shore power turn on the fridge and go outside and see if the burner is trying to light. You should hear the tick, tick, tick of the igniter trying to light the LP. If a flame does start and then goes out. A cleaning of the burner tube and orifice may cure the problem. By the way if the battery is not charged to around 12.7 volts DC that has to be corrected first. One last thing, are the interior lights working? If not, flip on the battery disconnect switch if there is one or find out why there is no power to the lights.
Sorry, the above is a broad brush approach but effective.