Agree about the battery, thus the reason I stated that 1 or 2 cells may be "dead"....Also recommended that he try another battery and THEN try to turn on 12volt circuit (lights), and try to extend the slides THEN....IF they won't extend, or no 12 volt output, will agree it's the power supply/converter/inverter....
Guess, with shore power plugged in, he could see if his 12 volt lights work...."IF" they don't, something is wrong with the inverter......no 12VDC output with 120 AC coming in...unless, as stated, power in side is fused and fuse is blown., (safety circuit), or breaker tripped.