Not very familiar with Delta airbrushes, but a quick search revealed that they've got all the major feed types covered. Is yours siphon feed, side feed, or gravity feed?
Did you try water before paint? If you tried the paint first, then tried the water, the problem could be paint clogged up in the nozzle.
Also can you gurgle it? If you're not familiar with it, pull the trigger back about halfway so you don't damage the needle, cover the nozzle with your finger or a folded up paper towel or something and then press the trigger down. This should force the air back into the cup and cause any contents within to bubble and gurgle. If not, you've got a blockage somewhere in the paint channel.
Safe bet is probably to strip it, clean the heck out of it, and put it back together again.
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