The "problem" - While plugged into shore power the fridge "ON" but not running on shore power. If Shore power is not available for any reason (to the fridge), it will try to light on propane to save your food.
There are 3 things it could be in order of probability:
1) The AC circuit breaker that powers the outlet that the fridge plugs into has tripped. Turn ALL the breakers OFF; then back on. If that corrects the power problem, the check light should go out.
2) The AC heating element FUSE had blown. It is located behind the exterior fridge cover panel on the outside of the camper (looks like the photo).
3) The "eyebrow" control board has locked up (or failed). Remove ALL power (including DC by pulling the fuse in the power center); wait 2 minutes and reconnect. This should reset the board. If that fails replace: Dinosaur Electronics Home. High quality circuit boards for RV appliances.
Lou and Laura with Bella - German Short Hair Pointer
2008 GMC Sierra 2500HD Crewcab SB Allison Duramax
2010 Flagstaff 8526RLWS - Superglide 3300
HAM CALLSIGN - KC3FFW