It is ridiculous that HP includes the purchase of ink cartridges as a troubleshooting step. The cost of cartridges is about $80.00. I have a HP4620 and it stopped printing black. I followed HP's troubleshooting guide to the bitter end and still no black ink. I then called HP support and was told that the solution to my problem was to upgrade my printer. Sorry about the $80.00 dollars that you just wasted.
Based on the Web traffic on this issue I believe this is a known issue with HP printers. HP should not suggest that throwing $80.00 at this problem is anything but enrichment to HP.
I will be upgrading but definitely not to an HP printer and due to this painful lesson if any of my other HP Products beigin to act up I will upgrade them as well. So Long HP.