Glad you were able to remove the cover...
A couple of things..
first, you should make sure the temp control is working, if that part has failed, the compressor will not come on. A quick way to test this theory is unplug the freezer, if it has a 2 wire temp control you can connect the 2 wires going to the control together with a piece of black tape, plug the freezer back in and see if it comes on.. if not, then it does sound like a compressor, start or relay issue.
There is a good chance the compressor has failed so if you invest $66 and it does not solve your issue you likely will not be able to return the relay.. you could go a cheaper route and purchase a universal starter/relay kit like this one at Appliance Zone https://www.appliancezone.com/rco410-refrigerator-supco-compressor-3-in-1-start-kit/
i used those for years, saved customers hundreds of dollars and for something under$20 you will at least know for sure if the compressor has failed or not and at least save about $45 in doing so