Certainly seems like a network issue It prints fine when you're connected over ethernet or USB?
I'd say try completely uninstalling all printers, reboot computer and even your wifi router, so they forget any corrupt printer settings etc. Then reinstall just the basic HP printer, whatever it says to do.
WPS... Isn't that the thing where you press the WPS button on the printer and then the same button on your router and it's supposed to automatically negotiate the two devices? That's the theory at least.
Ey Sam. I don't know this specific printer, but in general...
Be sure it is not connected with a network cable or a USB cable to begin.
It is likely that you can program the printer for your wireless network using the touch screen on the front of the printer. The SSID and Password that you program into the printer needs to match your wireless network exactly.
This printer may have the option to disable the wireless radio. Look around in that touch screen menu to be sure it is enabled for wireless.
Once you have the printer connected to the wireless network, download and install the latest software release for the printer.