Check out Frank's Fridge Maintenance doc at http://members.aol.com/Fkc43/fridge.htm
In particular, step 20, which reads:

"One more thing to check is the LED on the control panel.  It should be lit when the fridge is running.  If your sure the fridge is running, a simple method is to touch the exhaust pipe, it should be hot so be careful, and the LED is not working you need to check the single black wire, the same one we checked before, to the control panel and if your sure that is correct then you need to check the board.  Could be the board, LED, resistor or most likely the LM324, Radio Shack part #276-1711, chip which controls the LED on the control panel board is dead. The LED, resistor and chip can be replaced by obtaining them from Radio Shack then unsoldering and removing  the defective piece and soldering in the new one."

>Here's an additional question for all. If my frig LED wont light when it's running on
>propane, it has never lit up. What should I check to see if I can get that 'snowflake'
>LED working again?