Disassemble it. The needle is probably stuck in the nozzle. If it's in the nozlle, dip the assembly in the appropriate thinner and let thing sofetn up. When it comes loose, use pipe cleaners to clean the runs. If it's stuck in the body. when you're removed the nozzle, loosen the set screws at the back and tap the back of the needle on a hard surface to loosen it. Run thinner soaked pipe cleaner throught the channel and wipe off your needle withthe appropriate thinner. Hopefully, this will do the trick. he worst case I can see would be a bent needle or the need to replace the needle and nozzle assemblies.
If the paint is really tough and you have only metal part, you may want to use nail polish remover to clean the parts.