HP6940 won't print red with printer test nor photographic image. With cartridge 1, I refilled it, and I could see some red oozing (along with the other colors) if I press a clean tissue to the head. With a new reconditioned cartridge, same problem. No red. The other two colors look fine. Checking the printer options, no indication of red being intentionally removed. Also printer has been power cycled several times.

SOURCE: Cleaning the print head on my HP5440 printer?

Try cleaning the head of the cartrige with alcohol and a Q-tip, if this doesn't help you may have to buy a new one. Cartriges can dry up if they haven't been used for a while. Even though you refilled it, there could be some dry ink stuck in the head. Hold the Qtip with alcohol on the head for a bit and let it dry, reinstall it and then try printing again.

SOURCE: officejet d135 - "Supply Expired" error message

HP, in order to sell more ink, monitors the expiration date of the cartridges installed. Solution is either to buy a new unexpired cartridge from HP or to disable the date monitoring built in to the printer. This latter is done by removing the button cell located inside the D135 printer on the left hand side or by simply slipping a thin piece of plastic between button cell and metal contact. You will no longer have date function on printer, but it won't object to expired cartridges either.

SOURCE: HP 1610, Remove Cartridge message

also replace the colour cartridge as it is not showing but the printer is not able to detect that cartridge also.many a times it solves the problem.

SOURCE: Continue to receive "Remove and check black cartridge" message

Gotta love the internet!

I had the same problem...I seriously considered getting a new printer since I've had my faithful 5510 AIO for like, six years...but what I did was grab some witch hazel and a q-tip. Dipped the q-tip in, wiped down all copper contacts on the carriage and also on the print cartridge...blew on it to air dry...popped it back in and viola! It's back to normal.

SOURCE: HP 6000 Won't print with yellow cartridge

Try this :

Take out the power cable from the back of the printer keep on tapping the power button for 30 secs ; then plug it back.
Take out the catridges clean them with a Lint free cloth (copper contacts); also clean the catridge slot of the printer; put in back the catridges ;
Unplug the power cable from the back of the printer; press and hol down the (#) and the (6) button simultaneously with one hand and with the other hand put in back the power cable; and then release the (#) and (6) button;
It will perform a reset on the printer
IF still then it doesn't work then the catridge slot's copper contacts has gone bad and need to replace

Regards
Soumajit