I have basically the same refrigerator. Just to reiterate what Doug said. If you put the switch to Auto and the Yellow LP light comes on at all, the refrigerator is trying to run on LP. If the LP light is blinking it usually means the LP failed to light.
When you go outside and can hear the flame in the refrigerator, what is the yellow LP light doing? Is it flashing or on solid?
Definitely check for 12v at the plug in the refrigerator compartment.
And last thing, there may be nothing actually wrong with the unit. Mine will sometimes fail to auto switch back and forth between AC and LP when set to Auto. I see this most often when plugged in to the house while getting ready for a trip. If I'm on AC and I disconnect the shore power cord and then reconnect it again, the refrigerator will intermittently stay off with the LP light flashing.
