As most of the issues can be resolved by troubleshooting.Please see if the steps below help you:
HP displays a warning message when a cartridge is half full or is a third party cartridge. The goal of the message is to trick you to buy HP's new "genuine" cartridge. Although HP is obligated by law to let us refill the cartridge, HP planted some tricks. When we insert a half-full or a non-HP cartridge, the printer will display the message "Used or Counterfeit Cartridge." We can click "Continue," "OK" or "Yes" to dismiss this message.
Another HP's trick is to show a follow-up message: "Did you buy this cartridge as a New and Genuine HP Product?" The answer should be "No." If you click "Yes," then HP can stop you from using this cartridge. This message exists in some older printers. We put it here for reference.
The cartridge Is Low on Ink. Click "OK" or "Continue." If you are using a refilled cartridge, please note that this is normal and keep using the printer.
'Used, Refilled or Counterfeit Ink Cartridge Detected' Click "OK" or "Continue."
"Ink Cartridge Depleted." We need to turn off the chip info or "anonymous information" on the printer's LCD panel.
Incompatible Ink Cartridges. It is either an old version of the cartridge or a wrong model. You need to change the cartridge.
HP Protected Cartridge Installed. HP can let you "protect" your cartridge, so the cartridge can only be used in your printer. If you bought a refilled cartridge that is protected, then you won't be able to use it.
Furthermore, if the HP Printer Utility is installed on the computer, we can turn off the "Display HP Alerts."
You can check which cartridge actually has got the problem by Installing NEW Black with the old Color cartridge and see if it works and can Install the NEW Color with your old Black cartridge and see which cartridge is having teh problem and not printing. You can also try and clear the contacts of the Printer and the cartridge using a lint free cloth/ eraser/ alcohol. Just try and reinsert the cartridge for 2-3 times until it gets recognized.
First Hold the Power Button and then press the Cancel button on your printer and hold them together for some 5-10 sec. after that leave the power button first and then the cancel button. See if the lights stopped blinking and if the cartridge work.
Do not touch the copper-colored contacts or ink nozzles. Also, do not re-tape the cartridges. Doing so can result in clogs, ink failure, and bad electrical connections.
Please confirm if it helped or not so we can proceed further accordingly.