I have an fridge in my garage that quit working. Frigedaire frt21g4bw7 model.
I pulled the back off and messed with the wires but nothing happened.
The plug is good, the light still comes on but the fan is not moving and I have not heard the compressor kick on even though I cranked up the temp to see if it would kick on.

I do not feel like spending $200 to fix it but am willing to try something.

Any ideas?

Thank you in advance

Here is a quick and easy way to check this. If you open the refrigerator door, and get down on your knees, and where the controls are, right about in the middle is a small hole, and if you look in there you will see a groove, where you can get a flat blade screw driver, and turn it to the right, and see if the refrigerator comes on. If not, it is the thermostat!!! That is the part that you turn to make the refrigerator cold. So, if the garage is real cold, like most of the country the thermostat could be satisfied by temperature. But, like me, I don't have the time to waste, because I run so many calls in a day. Drop the control panel, if you like, pull the 2 wires off the thermostat, and jumped them out. Tom www.applianceeducator.com

Here are your parts, includes a wiring diagram.
Replacement parts for FRIGIDAIRE FRT21G4BW7 Frigidaire/refrigerator | AppliancePartsPros.com

The defrost timer is Item 23 in Section 3.
There is usually a hole in the bottom of the cover that will let you adjust the cam.
You have to adjust it slowly and they usually only rotate in one direction.
The timer should give a 30 minute defrost cycle every 8 hours of compressor run time. This is usually one revolution of the cam so do at least one revolution you should hear the contacts operating.

Be sure to have your freezer temperature set to the coldest setting.
The timer, compressor and fans all get power through the main thermostat so if it's contacts are not closed nothing will run.
If adjusting the cam does not get it started, then unplug the unit.
Remove the two wires from the main thermostat and short them together.
tape them up if you have to, to ensure they cannot short to anything else (most importantly, you).
Then try to force it out of defrost again.

One thing to note is that if the unit goes into a defrost cycle (compressor and fans off) and then the main thermostat remains open it could get stuck in a defrost for much longer than the normal 30 minutes because the defrost timer motor is not getting any juice.

Your ambient temperature is going to cause problems.
Cannot say if it is causing your current problems.
What happens is the internal temperature never gets warm enough to start the compressor.
So the unit does a defrost and the compressor does not start after the defrost cycle so the defrost heat stays in the freezer section and melts the food.
This is often not obvious other than ice cubes in a bucket sticking together but it can be a food safety concern.
Frigidaire does make a kit to overcome this.
It fools the thermostat into thinking the internal temperature is actually warmer than it is.

Another problem is if your ambient temperature gets much colder, then the lubricating oil in the compressor thickens and it does not get properly lubricated.

I hope the above is not too confusing but your problem is often just the ambient temperature.
Stick a hair dryer in the unit for a hour or so on medium heat and dollars to doughnuts it will fire up.

If it stays powered then it should be out of defrost in 30 minuites.