|Most likely the black ink delivery system (tubes & nozzles inside the printer) is severely blocked with dried-up ink which the driver cleaning cycle cannot clear.|
Inkjet printers must be used at least every alternate day to avoid this happening.
Remove the black cartridge and put a few drops of alcohol-based solvent into the hole at the bottom of the cartridge slot. Leave overnight, put cartridge back then try running cleaning cycle a few more times. If still no joy, I'm afraid it's new printer time.
Do not use petroleum-based solvents as they will soften and damage plastic/rubber components!