Hi, I am not sure which model Norcold you have but it sounds like it is a 2 source RV fridge (propane or 120VAC heater). The manual I have shows both fuses are 5 amp per the attached power board 2 source models shown. If you have a different model then you will need to check on line or in your manual.
So the fridge works on propane no problem, just the 120vac heater “seems” to have failed. You mentioned the fridge “outlet” has 120VAC on it......do you mean the two wires on the power board that feed the fridge 120vac heater element (marked AC Heater Terminals shown on the attached power board diagrams)? Or do you mean the duplex AC outlet inside the external panel of the fridge?
If you set the fridge for automatic and you are on shore power, (set your multimeter for AC volts at least 120vac); very carefully measure across the AC heater terminals on the power board. If AC is good feeding the heater terminals then the control board is probably good too and it is likely just the heater element is burned out.
To test the heater element continuity you must disconnect all shore, gen (off) and battery power (use/store off) from the coach and then carefully pull off one of the 120VAC heater feed wires from the power board. Use your multimeter set to “ohm meter” and see if you have any resistance reading across the heater terminals (one loose and one still connected to the board). If the heater element is burned out you should see open (no resistance reading) on the meter. If you check Youtube there are likely videos of changing out the heater element; or just get an RV tech or Dealer to do it for you.