All 6 computers and the HP 8500 were connected by Cat-5 Ethernet. It took several hours for the HP experts to figure it out. The solution is more weird than the problem.

Solution:
The Windows Firewall did not have all of the correct ports set up; BUT, the Windows Firewall was OFF, so it should have no effect. Right? Wrong!

To make the printer operate successfully, the Windows firewall needed to be turned ON, and the following ports had to be added as exceptions to the firewall.

Add the following ports thusly:

hp1 9100
hp2 9220
hp3 9500
hp4 9290
hp5 160
hp6 139

If you turn the Firewall OFF, the printer stops working. It must be ON. It is astonishing that the Firewall is NOT actually off when it is supposedly off.

David F Mayer