Hi Isabel Murnane,
My name is Lisa and I'd like to help you with your Officejet 4500. I understand you are unable to use your generic ink cartridge. When you say generic, do you mean that it is not a genuine HP cartridge? If so, I am not sure how much help I can be. Non HP cartridge may or may not work, we can not guarantee them to work as they are not our product. What you can do is use the following document to troubleshoot the issue:
HP Officejet 4500 (G510) Series and 4500 (K710) Series All-in-One Printers - 'Incorrect Print Cartridge' or 'Print Cartridge Problem' Message Displays on the Computer
Here's the thing, yes, you can refill your cartridges or use remanufactured cartridges, but you may run into problems.
QualityLogic, one of the world's foremost quality assurance organizations, tested the performance of HP inkjet print cartridges vs. remanufactured (refilled) brands. The results: original HP inkjet print cartridges far surpassed ink refills in both print quality and reliability.
Nearly one out of every six refilled ink cartridges tested was dead on arrival or failed prematurely
70% of refilled cartridges had some form of reliability problem
Count on HP original ink cartridges for consistent, worry-free printing. You may think you're saving money on remanufactured or refilled ink cartridges, but in the long run, the cost of wasted time, ink, and paper can more than make up the difference. -
Source
Most people think, 'well of course that is what HP or an HP representative would say', but I have done some research and found that many others have too. Here is a perfect example of somebody who does not work for HP in any way and basically is a customer advocate (in my opinion) ;
Should you refill your printer’s ink cartridges? HP says no (of course)
I found the above article interesting and genuine.
To summarize, again, yes you can refill the cartridges. The printer is not programmed to reject them. Sometimes the cartridges will not work and of course because they are non HP, HP would not be able to do anything to help. HP cartridges have a 2 year manufacture warranty;
Limited Warranty for HP Ink Cartridges and Customer-Replaceable Printheads for HP Inkjet Supplies , this may give you comfort knowing HP stand behind their product.
I hope this helps.
I work on behalf of HP.