If the nozzle is blocked, look through it with a magnifying glass up to a bright light (sky is better than a bright lamp). Suck the front end of the nozzle to remove any liquid and rotate it and with a magnifier see whether you can see any rotation on its shiny inner surface. You should not be able to see from its inside that the nozzle is being rotated. If you can, there is something stuck. Use an interdental brush (chemist) soaked in cleaner and gently pushed into the nozzle from its entry end. Re-check against a bright light. If the problem continues immediately with the first attempt at spraying, the supply of paint would seem to be the problem: either lumpy paint or something (a hair) in the passages or in the cup. When using any cleaning brush I inspect it against a bright light each time I insert it to check for hairs which can cause blockages. That includes the tiny bottle brushes sold for cleaning the passage between the nozzle and the seal in the middle of the airbrush.
Can you spray AB cleaner freely through the nozzle? If so, the paint itself might be the problem.
What air pressure are you using? Most people use 20 PSI. If you have a compressor, increase the pressure to max. This might dislodge a blockage.
You said "It's not a needle - when I remove it pressure is still low."
If the pressure is still low (by that I understand that only a little air comes out of the nozzle, when the needle is completely removed,) then there is clearly a blockage in the nozzle, or the air passage leading to the nozzle (usually hidden in the body of the AB). If in the air passage, I don't know of any way to access it. Perhaps putting the whole AB into a cleaner liquid overnight might help that problem.
Or the blockage might be in the paint passage leading to the nozzle, between the cup and the nozzle and further back towards the trigger. This can be easily cleaned as mentioned above by using one of those tiny bottle brushes sold for ABs.
"Today I am leaving all the parts in the water overnight - something tells me it's a nozzle...tomorrow will let you know if something changes."
Water won't do much. Use a cleaning liquid made for ABs. And obviously separate the nozzle and other pars from each other, and rattle the container from time to time.
If you have an ultrasonic cleaner, or know someone who does, put everything, disassembled, into it with a tiny drop of washing up liquid (to reduce surface tension I think). Use hand-hot water. Leave in the cleaner running for several minutes.
Edted:
I am puzzled why loosening the nozzle cap allows air to flow. Presumably, with the aircap tightened, the very tip of the nozzle and its hole can be seen just poking out of the front of the air cap. Could it be that the O ring between the inner end of the nozzle and the AB is old and being over-compressed and is being squeezed and so blocking the air flow into the nozzle.
