Hmm, I just checked in Devices And Printers to find that the printer wasn't listed. I selected the Add Device button and since it showed my printer, I selected it and it then sounded a connect .wav and appeared as it should have in the first place. I sent a test page to it and it printed it as well, but the tray icon still says that it isn't connected, and I don't find it listed in the Device Manager. When I added the printer as previously mentioned, it also displayed a window saying that it was installing a driver, and what I did find in the Device Manager was something called "WSD Printer Device" (whatever that is?) and it did print what I sent to it properly, but the tray icon still says that it isn't connected.
I also failed to mention previously that I tried to use the HP configuration utility to reconfigure the previous installation, but after a little bit, it said that it had failed, with no explanation of the failure. I would just try starting the installation over again and see what happened as if it were just a faulty installation, I don't think that would have happened on all three machines at the same time.
EDIT: Just checked the HP directory in the Start Menu, and the configuration utility nor the uninstaller are not visible any longer.