It sounds like you have some general AC wiring problem. I find your descriptions are quite confusing, either because the problem is very confusing or because communication isn't happening.
The fried GFCI is IMHO most likely due to a bad connection on the line or load connections to it. I may be wrong, but that seems most logical to me. I would assume that the load line from it goes to other outlets or AC items, perhaps including the converter and/or fridge.
Maybe the fridge is misbehaving because the converter is producing an improper voltage? Do you have a good 12V battery hooked up—and if so, have you verified that it is still good?
At any rate, it may or may not be that your converter is fried, and/or that you have other wiring problems in the trailer. If it were mine, I would be hesitant to use the 120V electrical system until I (or somebody else who was qualified) understood what was going on and had fixed the underlying problem(s). I'm not fond of potential/possible electrical fires.