sounds like a burnt out relay or bad compresser. first thing to check is the start relay and overload. these are what actualy attaches to the compresser. unplug the refer and pull the relay and overload. you can probably shake it and listen for a rattling. if it rattles the bi-metal overload disk is shattered and you will need to replace. once you have replaced that( if it is in fact the culprit) you need to check how many amps your compresser is drawing in both start-up and run. using an amp clamp ( can be picked up at alot of hardware stores) clamp it on to either lead going to the overload and relay. 6-8 amps on start-up is a bit high but ok higher than that your compresser is wearing out. 1-3 amps on run is ok, higher, again worn compresser. if all is within specs you just had a overload/relay wear out. good luck and post your results here

if anything your compresser may have fouled the relay and overload, though it isn't certin.replace the overload and relay, then check to see how many ams it is drawing. if excessive then you may have a bad compresser. post your results here