Hi fraun,
Welcome to the HP Community, I hope you enjoy your experience! To help you get the most out of the HP Forums I would like to direct your attention to the HP Forums Guide First Time Here? Learn How to Post and More.
I understand that your new black ink cartridge isn't working correctly. I will be happy to assist you with that. I have included an HP document on Troubleshooting Print Quality Issues including not printing black ink. If this document doesn't resolve the issue then contact HP Total Care at 1-800-474-6836 in North America or visit this link outside of North America because ink cartridges have their own warranty and can be replaced.
Thank you,