Centurion converters have been known to go bad. Do you have a battery connected to the trailer? The items you describe that work are 110v, and the interior lights and refrigerator need 12v to work. The A/C will only work on 30 amp, you could do damage if you try to run it only on 15.
The converter does have a small 12v output to charge the battery, and without a battery hooked up, you should be able to run a few lights at most. If that 12v output has gone bad (often what seems to fail first), it won't put out anything, which means it won't charge your battery and it's only a matter of time before your lights and things will drain it completely. Also, without a battery connected, nothing would work.
If you do have a battery on the tongue, it's possible that it's completely dead. If you didn't disconnect the battery when you parked it, and if it wasn't plugged in, the LP gas detector will drain the battery in just a couple days. Sometimes you can charge it back up, but draining it completely and it staying dead usually isn't good for them.
A Progressive Dynamics converter seems to be the popular replacement, even though I don't have personal experience with replacing one.
2007 T-286SR Cherry/Granola, #6236, original owner, current mileage: 9467.8 (as of 5/26/19)
1997 T-2653 Blue Denim, #5471
1979 12 1/2' MC, Beige & Avocado, #4639
Past Sunlines: '97 T-2653 #5089, '94 T-2251, '86 T-1550, '94 T-2363, '98 T-270SR