I like many am a great believer in re-cycling my old printer cartridge and re-use by filling up with my own ink. HP on the other hand want me to purchase a new cartridge and make life difficult for the Re-users by not showing the re-plendished ink level.
I know that there are 'Zappers' out there or chips that are supposed to do just that but as yet I can't find one for this printer.
Google is indeed a friend sometimes, but not on this occasion I feel as I have not been able to get the answer I am looking for I'm afraid. I don't think for example that the HP C4280 cartridge is of the 'Zapping' type as the history is recorded either in the printer itself or more likely in the operating software.
In the hits from Google there were codes that could be entered to reset, but I'm not sure I saw your model # among the solutions posted. And the codes were very different from model to model.
I think you have to research the refill capability before you buy a printer, if possible. Or go laser and even then you still would need to do your research. I went to a little shop that does refills and asked the owner about brands and models.