Three black cartidges won't print in an Officejet 4630

[EMedic]

First, MacOS 14.6.1 Sonoma is not an option in the pull-down Operating System window.  I use Sonoma with a Mac Mini 2020.  Now, to the point.

Any number of combinations of genuine HP cartridges or remanufactured cartridges, color and black,  result in the printer display screen reporting that either BOTH the color and black cartridges need to be replaced OR just the back cartridge needs replacement.  A color cartridge (whether remanufactured or genuine HP) works okay in the single-cartridge mode.  But not one of the three black cartridges, genuine HP or remanufactured or in single-cartridge mode, will print,  And all three black cartridges result in the "replace cartridge" display on the screen.  I have performed all the troubleshooting steps specified by HP, down to resetting the printer (unplugging the printer while it is turned on, waiting 60 seconds, then plugging it back in — nothing works.  Can anyone suggest a remedy?  I need the 4630 because it is a fax machine, too.  In dismay, I bought an Envy 6555 to be able to do faxes again since the HP phone rep told me by phone that the Envy 6555 does faxes, but when I got it, it does NOT.  By the way, though the Envy 6555 does not fax, it is a great little printer for the price.  But I need the 4630 to operate as a fax machine!   And, yes, I reloaded the Firmware and drivers from the HP site.  What am I doing wrong, or what else needs to be done?  Thank you in advance.

H—E—L—P!