Turn off WEP it is not secure. Also you should not have conflicting security protocols on your router.
without all these replies making it more difficult you need only do the following to get your HP printer to function.
1) go to the HP printers drivers and set up page.
2) run the setup program for the printer and select the wireless LAN option. It should find the printer. If it does not then it will instruct you to setup with a printer cable.
3) the printer will find the correct settings and it should be verified as connected prior to you taking the cable off.
Now you need only test the wireless connection with your phone via looking to see if the HP is listed. The same holds true with your wireless laptop or desktop after selecting the printer from the printers list.
Oh I forgot to mention during wireless setup you will need the SSID password to connect. Enter it exactly or it won’t connect.