The black ink nozzle in the printhead is probably blocked with old, dried ink.
Try clearing it with the nozzle-cleaning utility in the printer driver.
If the blockage is too severe for that, remove the printhead and let it soak in warm soapy water overnight. Then rinse it thoroughly and allow it to dry naturally (do not use hair-dryer or other heat-source).
I'll have to see if I can find what you're talking about and try cleaning it. I did call HP and after many tests and cleanings they decided it's a hardware problem. Thank you though.