the problem partially has to do with the contacts in the switch and the plug getting dirty and going bad over time. The contacts go bad, and the computer doesn't see the resistance values it's looking for so the AC doesn't come on. I replaced the fan speed switch once because i thought it was the problem, and my AC came back for a couple weeks but then it went away again and was back to only working one 1. Still worked if you set it to like 2.5 or 3.5... but the problem's still there making your switch and the plug it goes into worse. Recently, i replaced my entire HVAC control thingy with one from a 2003 protege- i sprayed some contact cleaner in my old switch (which was in pretty good shape- contacts looked nice and clean) and now it works... it's either the cleaned switch or the little circuit board (i think it's just the cleaned switch) that came with the new heater control unit that's making my AC work again, but i know in a couple weeks or months it'll start flickering on speeds 2 and 3, then just stop working completely on those speeds.
On the junkyard car i got the climate control unit (i've got 3 names for it) the plug that the fan speed switch plugged into was completely toast... all melted and s***. Mine's just a little melted... but the current going over the fan speed switch contacts is actually enough to the point where if the contacts are bad/dirty heat can build up and melt your plug. Replacing the switch is a lot easier than the wiring... or, at least i imagine it must be. I don't want to find out where those wires go, but i imagine it'll give me a headache.
So, take out that switch and give it a good cleaning yo... and make sure your plug isn't melting.
Too hot in the black on black hot box? Ya know, in that 2nd batman movie... when the joker blows up that guy with that stomach bomb to get out of jail, he's drivin' (or, at least some dude's drivin' him) off and he's stickin' his head out the window. He's shaken' it around and s***, so i can only assume he's trying to cool off because that cop car must have a similar problem. You could give that a try too if you can't fix the AC.