The fridge electronics and lights operate on DC. When hooked to shore power or running the generator your fridge can operate on AC (the AC used exclusively to power the heating element).
Query - are you hooked up to shore power when experiencing problems? And what settings are you using on fridge (auto or gas). The "check light" implies that your fridge has failed to ignite propane and you normally won't see that if your connected to shore power assuming you have the auto setting on the fridge. The lights dying after a few seconds would imply DC power issue .... have you had your batteries checked?
