I think "reservoir" is the word, but anyway, it sounds like the main nozzle is completely blocked, this would cause the airbrush to back up through the reservoir (you can see this for yourself by blocking the nozzle end with your finger and pressing the trigger.)
FWIW, I hardly ever take my airbrush apart for cleaning. Instead I spray lacquer thinner through it till it runs clear, then Windex. (Ammonia-based window cleaner). I spray into a cleaning jar like Iwata makes. I've had the same kind of airbrush since I was a kid -- A Paasche VL -- old school nowadays, I realize, but it works just fine. I've had the current one for at least 20 years, same nozzle, same needle valve. On the Paasche VL model anyway, there are passages that never touch liquid in normal operation and soaking the disassembled parts in solvent actually risks plugging the air passages. Your mileage may vary!