Does your printer software have an alignment procedure? With my Canon printers, they normally prompt me to run through an alignment procedure after replacing an ink cartridge. With my Canon BJC-3000, I can also start that alignment procedure by going to Control Panel, Printers and Faxes, selecting the printer, right click on the printer, select Properties, and then select the Maintenance tab. I have an older BJC-2000, I do not have a alignment option for it via Control Panel. So, the options will vary, depending on your model printer and your printer software.
Since your printer is out of warranty, I don't know what you can expect from HP as far as support goes. Probably not much, other than maybe FAQ or Knowledge Base info on their website.