Well, before you write off the airbrush, take a nozzle that you know works and try it out. If it works, then you're in the safe zone, but just take good care of it, as the brush and nozzles really need to be cleaned well every time.
If you were using acrylics, just plop the nozzle for a couple of days into windex, and it should disolve any paint left. Just take the actual needle housing out of the casing that screws into the AB body, and soak them both.
I had a similar problem with my first Aztec, but to be honest, I'm not sure what the problem was. I'm going to assume that they didn't send you a broken one, so the AB shouldn't be the problem, but rather the nozzle.
As for your other question, which compressor are you talking about? If it's the testors mini-blue compressor, I have no idea. I have the same one, and am wondering whether it will work. I have no reason to suspect that it won't, as the only thing you need is a proper adapter. I'm not sure how strong (in terms of PSI) the thing is.