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There's an in-line fuse on the positive cable near the battery that you'll want to check. You say switches on the panel are lit so chances are the fuse is OK but check it to be sure. The overhead light each have switches on them, have you tried flipping those? There's a fuse panel inside the trailer - buy some auto fuses (5, 10 & 20 amp) and change them out with new. If nothing comes on, you may have a problem with the converter. The converter charges the battery when on shore power and distributes the 12V power to the trailer
I'd be concerned the prior owner didn't use a battery as it kind of a requirement when towing.
2014 Eagle Premier 331RETS
2016 Silverado 3500 DuraMax/Allison
1975 Corvette & a couple ATV's