Here's the Linux Printing page on this printer:
Here's HP's drivers page:
I glanced at this HP page
and it wasn't immediately clear whether it had wireless networking or just ethernet.
I would suggest giving it a static IP address; that makes it easier to set it up on the computers.
Once you get it on your network and can ping it, your computers, whether Windows or Linux, cabled or wireless, should be able to print to it. My HP L7680 works flawlessly with HPLIP.
Did you install the HPLIP graphical user interface? It's often a separate package from HPLIP itself and makes working with HPLIP if you haven't used HPLIP before.
Edit: Once you install HPLIP, you still must set the printer up in HPLIP. The mere presence of HPLIP on your computer does nothing.