re: Frigidaire Professional Line Fridge

You need to see if there is 115v going to compressor. If so. Replace the relay on the compressor. Unless there is a Grey box attached to or near the compressor. That's an inverter. If it's getting power by compressor isn't running. Check the smaller plug for voltage. It should constantly be changing from 2v to 5v. If it tests no volts then main control is bad. If you have 115v plus a range of v voltage on the control wires then the inverter is bad. Likely it's a bad inverter that's a common fail point.
Ditto with the relay. A relay is a lot cheaper.
An inverter board can go up to $200 a relay can be a cheap as $15.