Yesterday I had an auto update from HP for my AIO. I suggest downloading and installing the newest HP utility. I also had issues printing to an HP and my resolve (last week) was to force an IP number on the Virtual that made the two (Parallels and Printer) within the same subnet. Is your printer USB connected or ethernet connected and to what? My printer was hard wired to a router.
Its hooked to Imac via usb cable, figured out in windows seven that I have to turn the printer on after windows has booted up. Not a cure but that worked, still have issues in xp? Just wished it worked like my mac
Mac Printer connected to the virtual machine's printer port.
USB printer connect to the virtual machine's USB controller.
Network printer accessible through the virtual machine's network connection. Does your printer have an ethernet port?