The function of a converter in RV is...convert 120VAC into 12VDC(could be 24VDC/6VDC according to manufacturers). When this converter is defect, nothing of 12VDC will work(lights, 12vdc pwr supply outlets, ceiling fan...). If the coverter is plugged in 120vac source and some of 12vdc equipments don't work at all, the problem falls within those individual equipments(light bulbs, fan...). I suggest you should check, first thing at the fuse panel of 12VDC AFTER checking out each of those failed 12VDC equipment. If the converter has a stored-in
battery, it doesn't have to be plugged in 120VDC in order to supply 12VDC output as longas it's bttery is full enough. If the converter is total broke down, nothing will come out as 12VDC from it. Hopefully it helps. If your A/C works with 120VAC pwr supply, regardless of converter state, A/C will still work independtly...