Can't add HP Deskjet 5940 as a wireless printer

I would like to use an HP Deskjet 5940 through a Netgear WGPS606 wireless printer router but can't add the printer via the Printer Setup Utility -- the printer doesn't show up on the list of printers to choose despite having downloaded the latest driver from the HP web site. I've successfully added a Brother printer that is available both to my Mac and two Dells. I can also use the HP printer wirelessly through two Dell desktops. I've downloaded the latest Mac printer driver for the HP printer and can print using the 5940 if it is connected directly to my PowerBook G4 (Mac OS X 10.3.9) via a USB cable. Is there a problem with my operating system? With the Printer Setup Utility? With the latest HP Deskjet 5940 printer driver downloaded from HP? An expert at an Apple store suggested that this means that the printer driver doesn't support wireless printing and thought that I should try another HP driver; has anyone had success with another driver for this particular printer? Any other suggestions or tips to get this particular printer to work through a wireless network? Thank you in advance for any assistance.