Hi @warlock1
Here's an image of the wiring diagram for the refrigerator that will help.
I'm thinking that rather than the compressor being the problem, more likely it is one of the following components as any one of these going faulty will prevent the compressor from starting.
If one of the following components is faulty, search online using the part number only, to find suppliers that suit you best.
If you have a DMM (digital multimeter) you can test if they're OK or not but be aware this may involve testing when lethal AC voltages are present. If you don't know what you're doing then don't do it! Contact a reputable, professional appliance repair service and ask for a quote.
a) #1 in image the PTC relay aka start relay - part #WP10097204
b) #2 in image the defrost timer - part #WP68233-3
c) #3 in image the temperature control aka the cold control thermostat - part #WP61001673
d) #4 in image but less likely as the compressor would try to start but can't keep on running, is the run capacitor - part #WP65889-4
Troubleshooting steps with the power connected to the refrigerator :
- If the condenser fan near the compressor and the evaporator fan (aka freezer fan) are running, then the defrost timer and the temperature control are both OK. Disconnect the power to the refrigerator and then remove the start relay and gently shake it. If it rattles it is faulty and needs to be replaced
- If they are not running it may be a faulty defrost timer or a faulty temperature control as either will also stop the compressor from operating. If you can hear the defrost timer motor operating then the temperature control is OK but maybe not the defrost timer i.e. faulty contacts in timer
(click on image)