TonyTiger - If you are getting a reading on your Ohm meter other than "1", then you have an internal short from one of the hot leads to the ground terminal. The Ohm reading or value would only tell you how good the connection is. You have already discovered the problem.
As I mentioned in my previous post, be sure you are not touching the frame of the fridge (while plugged into AC) while touching any other good connection to ground as the electricity will flow through you.
I would suspect that your fridge works fine when plugged into a non-GFI receptacle, but it is a potentially dangerous unit.
I'm not familiar with the Norcold fridge, but I would start by finding where the power cord connects to the fridge (not plugged in). Using the Ohm meter you should never have a reading between those connections and the frame of the fridge other than a "1" - just like if you are not touching the two prongs of the Ohm meter together. I would then do a close visual inspection to determine how the electricity travels through the unit looking for some contact to the frame of the unit or ground. Somewhere in the circuit you should have a heating coil and I suspect that it has somehow shorted to ground.
I had a similar situation with my water heater. It worked when we got the motorhome, but the next time we tried to use the heater a fuse would blow. Tracing the electrical circuit on the water heater, I found the problem where the wiring connected to what I call the temperature of the water sensor. The sensor had slipped out of place and the sensor was touching the steel tank. Moved it to where it should be and problem solved.