I assume you have the correct driver for the printer. With HP printers, I prefer to use HP's own (with HP's, run dvd/file as a complete setup - less problems). So if the installation disk isn't at hand, download the correct driver from its mfr's site and save it.
1. Goto Device Manager and Uninstall the printer. Disconnect printer from computer (unplug).
2. Roboot for the 101th time ...
3. This is Optional: Install the utility program(s) - if you need them.
4. Connect the printer to computer. Windows will 'find' the new device (msg in lower right corner) and find its driver (if windows has one in its database) or it will open the installation window. Don't let it search online, direct it to the folder/drive where the (downloaded) driver resides.