The refrigerator will not make any noise as there in no compressor.
It actually works from heat ( i know, sounds funny). After the electric thermostat the power goes to a heater which heats the ammonia solution used in the cooling process. You should be able to feel warmth in the same area as the gas burner.
If you do not you should see 2 leads coming from an insulated compartment near the burner. You should have 110 there. If you do and still no heat measure the resistance as you could have an open heater.
Try running the fridge on gas and see if that works.
Allow several hours to feel the temp dropping in the freezer. It takes a while to cool down. Also the fridge needs to be level to work properly
Rick Davis 1602 K8DOC
61 tradewind, plus a few others
13 Ram 2500 TD
99 Dodge TD 577K miles