It sounds to me as though the compressor is on the fritz. It seems highly unlikely that both the AB and compressor would break at the same time. Since I can't think of anything that the AB could do to caues the compressor start up problem, my money would be on the compressor.
Need more info. Some diagnostic things to try to fet a better handle on the problem, would be to take the hose and AB off the compressor. Try an start the compressor. If the problem is still there, it's definitely the compressor.
If the compressor actually starts working without the hose connected, try connecting the hose but without the airbrush. Maybe the hose is clogged and excessive backpressure is causing problems?!? just wild guess, grasping at straws..
If you have a pressure guage, what is it showing during all this?
If the compressor and hose are working correctly without the airbrush, then presumably something is wrong with the air valve and /or trigger. Get out your instructions, and disassemble that part of the airbrush and see if the problem with it either fixes itself or becomes apparent.
Good luck.
Andy