Without a voltmeter any diagnosis will be just a guess. I would imagine even the least experienced RV tech would know how to at least do basic voltage checks at the converter's input and output. Many of the items you mentioned require heavy current draw and are many times wired directly to your battery which sounds very depleted at this point.
Run down to Wallys or Harbor Freight and pick up a cheap battery charger to get your batteries back up, for a few bucks more grab a voltmeter too. Let batteries charge for awhile hopefully this will restore some DC items, heavier current draw items will require a deeper charge on the batteries to function properly. There are fuses located near the battery, use voltmeter to trace circuit.