I'm sorry, I forgot to mention about the wireless part. My error.

Update the firmware in your wireless router. Manufacturer's website, make & Model needed.

Broadcast SSID(You may want to change this to make it easier to connect)

Use WPA security

Mixed b and g mode(n if available)

Use channels 1, 6 or 11. Most devices work better on these channels.

Now when you go to install your printer, choose network. Then follow the instructions.

Try installing it this way. Then tell us what you get.

Disconnect your printer. Go to start/programs/HP printers and un-install your printer. Now go to the control panel and make sure your printer is un-installed.

Restart your computer.

Now go to here download drivers and utilities.

Install your printer. You'll be prompted when to connect it.