Saving my 84 Norcold Fridge...if possible

That model uses a mechanical combination gas/electric thermostat- no electronics at all. It does look like a "will fit" substitute is available, but it *really* takes someone that knows what they are doing to replace it.
I would first unhook the heating element, test for continuity, and hook it directly to 120 volt power- bypassing the all of the controls (of course, this is after checking the basics of venting and power).
If it gets cold then, the problem is in the controls. If it doesn't, the cooling unit is bad.

The part number for the thermostat is 614376MC - google will give bunches.

Norcold was very friendly. But could not even suggest a replacement part. Found that odd but darn was she friendly to talk to. Great call...just no help overall. My 84 fridge may have been replaced with an old 1977 model as she said the model number indicates it is really that old. Can't complain about 37 years of faithful service. But I am really gonna miss this old lady if I put her down.

Norcold also has a pretty good Tech department, so you might be able to call them with the information you have on that fridge, and they may be able to direct you for the parts you need, or at the very least, help you troubleshoot the issue.

Should be a service manual on Chris Bryant's Page.

If it's like newer fridges, a Thermistor that is failed "open" or "high" will cause the unit to cool continuously. IF that's true of your fridge, then simply unplugging the 'mistor from the board should cause the fridge to run.

There's a replacement called Snip-the-Tip that many here have had good luck with.

But look at a manual, see if fuse(s) blown etc.

And...WELCOME!!!