I know have three black cartridge full of ink. I still cannot print. It has been one month. What

[marcodiego]

Error message:  "There is a problem with the supply system.  Try replacing the affected cartridge [black] with a different, non-empty, cartridge" This is the third time that I have installed a black cartridge--full of ink.  I haven't been able to print for a month.  What do you suggest that I do?  The people with whom I spoke in India and the Philippines have been no help.  And there's no way of calling you in the U.S., apparently.

[BeemerBiker]

I am guessing the ink is not HP.

Non HP ink can be used on this list of HP printers.
The below type is unlikely to work.

Check the expiration date of the ink and verify it is genuine. To check if an HP ink cartridge is genuine, look for a security label on the cartridge, scan the QR code on the label with your phone, and then go to HP's website hp.com/go/ok to verify the serial number on the label; if the label appears tampered or the serial number doesn't validate, the cartridge is likely not genuine.

See if EWS can provide more information.
This explains how to Use the HP printer Embedded Web Server (EWS)

General ink cartridge help

Did you sign for instant ink?  For any of the "plus" features of an HP printer?

Possibly the ink in the printhead dried out.