The fridge uses 12v for its controls (temperature etc) when on either gas or electric. It will use less 12v on AC with no propane burner to power.
12.2v on the resting battery means it is half full. needs charging up so it won't sulphate. (Was on the shelf at the store too long)
You can get by on shore power by just staying on battery and charging the battery up every so often with any old charger. No need to rush out and buy a new converter at twice the price of ordering one on-line for a good price.
Not clear when you swapped the battery, but the two 30a fuses were the "reverse polarity" fuses that can be blown when installing a new battery and getting the wires mixed up.
If the converter is a plug in to a receptacle, try that receptacle with a plug in lamp or something to confirm it is "live" (if it is on a GFCI circuit, reset that) --and or plug the converter into a different receptacle known to be live--use an extension cord as required.
1. 1991 Oakland 28DB Class C
on Ford E350-460-7.5 Gas EFI
Photo in Profile
2. 1991 Bighorn 9.5ft Truck Camper on 2003 Chev 2500HD 6.0 Gas
See Profile for Electronic set-ups for 1. and 2.