Welcome to the HP Forums. I would be happy to help you with your HP OfficeJet 6500A Printer. I understand that you are getting network connection issue and you have already done some preliminary troubleshooting.
Restart the computer, printer, and router.
Check the network and printer connection status.
Manually connect the printer to your network.
Run the HP Print and Scan Doctor.
Temporarily disable firewall software on the computer.
Uninstall the HP driver and software.
Reinstall the HP software.
Click here and refer the document to perform the above steps.
Let me know how it goes.
Cheers.