Model and serial number are listed inside the unit and on the back. You can then search for the correct replacement. I'd recommend an Isotherm or anything with danfoss compressor. Very quiet and runs on a lower amp load then the factory Norcold...
Easy to replace a Norcold,but not cheap, but as an option, I use a portable Engel refridgerator /freezer. The good ones work great and run on 12V or 110V. We use ours a lot as an extra. They run about $650, but are very quiet and reliable. They hold about 30 cans of soda to give you an idea of the size. Check the web for Engel Portable Refridgerator.
Canuckohio