Use these steps.
1. Start with the battery itself. Have it tested for shorted cells.
A shorted battery can act as a very large resistor. It will eat up more power than what the converter can put out. Thus, appliances that are sensitive to specific voltages, won't get what they need to operate. Non-sensitive items may function normally, or, they could have limited to no function at all.
2. If battery is good, move on to fuses and breakers.
Do not trust a visual inspection of fuses. They don't always look blown. Test them with a meter. Don't forget the fuses / breaker outside.
3. If all fuses and breakers are good, determine the 12 volt circuits for non working appliances.
At the distribution panel, test voltage accross terminals where your fuse would plug in.
If you have good voltage, work your way towards the non working appliance.
If you don't have good voltage, work your way towards the battery.
4. Disconnect power, pull converter / distribution panel out of the wall, and look at the rats nest of wires behind it. There may be some in-line fuses that need to be checked.
5. Outside the trailer, remove access panel behind the fridge. Look for more fuses.
Hopefully, you'll find the fix on the early steps.
I had a shorted battery problem with my TC. Only thing working, was one dim light. Turn on more than one light, nothing (12 volt) worked. This was with or without shore power. All fuses checked good. I disconnected the battery and found everything worked on shore power. Just out of curiousity, I hooked my solar panel straight to the converter (no battery) and lights worked, 12 volt television worked, bath fan worked. Furnace and fridge, did not.