From “Cartridge Expiration Date Workarounds“:
In light of the lawsuit against Hewlett-Packard over the expiration date of their cartridges, two ways to fix the problem:
1) Remove and reinsert the battery of the printer’s memory chip
2) Preemptive: Change the parameters of the printer driver
Search for hp*.ini … In it there is a parameter something like pencheck. It is set to 0100. … Set it to 0000 in the file and save the file and REBOOT.