The air conditioner works off of 117VAC. If plugged into shore power the air conditioner should work. If it does not that means you have to find out why the rig has no 117VAC power coming to it. The connector you plug your rig into for AC power (shore power) may have blown a fuse or tripped a breaker in the house or garage electrical panel. If those are good find the rigs power panel inside of the rig and push the 30A breaker lever firmly to off. Then push it firmly to on. The air conditioner should now turn on. If it does you should have lights and the fridge will be happy. If you do not have lights that would point to a bad converter/battery charger. I know on my Chateau I have lights when plugged into shore power without the house batteries connected.
Everyone should have and learn how to use a cheap digital volt meter. They are from $15 to $20ish and sold even at Walmart. They have an on/off button to turn them on. They have two leads. The black one goes into the COM connector and the red into the V/Omega connector on the meter. There is a rotary knob you turn to the 20VDC setting (read manual). At this point you put the red lead on the battery positive terminal and the black lead on the negative terminal. The meter will read the volts your battery is charged to. If it reads 13 or more volts your converter is trying to charge you battery. If it reads 12.2volts your battery has no charge and the converter is not working. Well, on my Chateau the converter charges the battery even with the salesman switch off. So plugged into shore power the batteries will measure around 13VDC.
If the above looks good and you do not have lights when unplugged from shore power. You may have my problem. I have had an issue with the salesman switch on my rig. It likes to blow a 5 fuse on the 12VDC transfer relay every year. On my rig that is under the forward seat of the dinette. That seat has all the electrical breakers and fuses for the rig. There is a panel under where your legs would be while eating. I just replace the fuse every year. I paid to have it fix, NOT. Fuses are cheap. There are two 5A fuses physically on that switch (the switch looks like a small volcano just sitting behind the fuse/ breaker panel) and one blows every year.