Paint occasionally does manage to get down in those valves, but you can usually feel it by the trigger being sticky when you push it down. They are simple little mechanical valves, and usually if the trigger does move down when you push it air will flow. But, stranger things have happened ...
Unscrew the valve from the airbrush body (you may have to use pliers to get it loose) and screw it into your airhose. The top of the valve is a cone-shaped piece of brass. Push it down with your finger and see if you get air. If so something is plugged inside the airbrush itself since you have indicated that the hose and airsource are OK.
The valve has five pieces to it. It's easy to disassemble but it's also easy to lose the pieces so be careful.
Hold the valve assembly with a pair of pliers on the knurled ring around the outside of the body. Look on the bottom (the part that screws into the air hose) and you'll see a hole. That hole is shaped to fit an Allen wrench (not sure what size though). Use an Allen wrench of the appropriate size to unscrew the bottom cap. Inside there is just a brass plunger with an o-ring around it and a spring. Clean everything up (I use laquer thinner on everything except the o-ring), put a little airbrush lube or Vaseline on the o-ring, and reassemble and it should be good as new.