The multi-power type fridges (120VAC-Propane-12VDC) require 12VDC to operate the Dc control board and some also operate the lamps inside the fridge. This way you can run the fridge off of propane when camping off the power grid.
Check the interior lamps - hopefully one of those has blown causing your short. The 12VDC Fridge control board are also known to blow to cause this same kind of problem.
Another failure might be the on-board converter is acting up and may have put out 19VDC instead of 13.6VDC which may have blown the Fridge DC control board??? Need to check the DC volts level coming out of the converter unit as well. Should normally read 13.6VDC when plugged into shore power.
My first thing I would do is pull out the fridge interior lamps and inspect as well as the socket they are plugged into... A black burned glass indicates the lamp has failed. If the lamp socket has over heated then you will have to remove and replace that with new lamp socket. Those automotive type incandescent bulbs really put off some heat when being used.
Plugging the fridge into a separate extension cord will not power up the trailer fridge fridge if the DC CONTROL board does not have power.
Also unplugging the fridge from its 120VAC receptacle will have nothing to do with the 12VDC Control board.
just my thoughts...
Roy Ken