This has become more-or-less common knowledge on the Net, but for my own convenience in searching (and in case you didn’t know), the way to remedy an “Incompatible Print Cartridge” message fro your HP Photosmart C4480 printer is to:
1. Simultaneously press both the X button and the power button and hold
2. (NOT simultaneously) press BLUE button then GREEN button then GRAY button (in that order)
3. using blue (or grey) button, scroll-seek to the “information menu” – press OK button
4. press grey button once for “checksum for relock data input” – press OK button
5. press (X) repeatedly until you return to the normal main menu
(Instructions from this YouTube video.)