Brand new battery.......so you should have 12V DC to RV.
Converter bad........so it can't supply DC system OR charge battery
Unplug it/disconnect it from AC power source. It is just a drain on AC system.
Fridge will run on AC power with RV plugged into AC power source....battery will supply needed 12V DC for fridge control circuit BUT only for a while cause trickle charger won't keep up with drain on battery.
Will need to put a battery charger on it IF you plan on running fridge or any other 12V DC items....until new converter.
AND when you hooked up that new battery......hope you connected it without swapping +/- cables.
There are 'reverse polarity' fuses on converter that will blow if battery connected backwards and then you will NOT have any DC inside RV.
WHY do you NEED to run fridge?
Hope RV is level..when running fridge or you will have more expensive issues