I had one printer that allowed me (meaning, its drivers and related printer control panel)to disable the black cartridge and only let the color ones to be used. When I tried to disable the black cartridge, just out of curiosity, I had a similar problem as yours (black no being printed), even though I thought (and still think) it made little sense - I would expect the setting to cause black to be printed via the other colors rather than via the dedicated black cartridge, the option being needed when you're out of black ink; but instead I got no black at all. Or, I did not get the purpose of that specific setting.
Could this be your problem?
Admittedly, it was many years ago. It was na HP printer, but can't remember what model. Desktop, personal, inkjet, however.