OK - thanks for the helpful info.
I guessed that was probably the cause.
Will get a couple of cartridges ASAP.
I hope that is enough to fix the problem. Near as I can tell from HP's horribly non-informative Web site, your printer has a separate print head, the print head isn't part of the ink cartridge. That means that even if you put new ink cartridges in your printer, if you don't remove and clean your print heads, it isn't going to print.
I haven't found instructions online for how to remove your printer's print heads to clean them. But cleaning the print heads in some inkjet printers can be a bear. You have to remove them and soak them overnight in a solution of ammonia and alcohol, and then rinse them. You may need to repeat doing that a few times if they are really badly clogged.
Just FYI, inkjet printers are worthless to folks who don't print regularly. And by regularly I mean probably once a week or so. Even the more recent inkjet printers that automatically park and seal the printheads to try and keep them from drying out, need to be used fairly regularly.
If you only print things once every three years, it might be best just to forgo having a home printer and to send your print jobs to a local service bureau, such as the ones in most Staples.