Mike on Maui: What a neat user name! Firt, let me say how much I appreciate your response. I'd love to learn that my troubles are due to bad settings or cables, or something that's easily remedied. I fear that's not the case.
My present situation is that I have a 'good' G4 (466 MHz) to compare with the 'suspect' G4 (400 MHz) with the questionable ethernet port. Each have ethernet cables connected to a router which is then followed by a cable modem for internet access. In addition, I have a left-over hub for diagnostics.
When both are connected to the router: Good one lights up its port light and makes internet connection. Suspect doesn't - with either of two ethernet cables.
When both are connected to the hub: Port light-up is as above.
Look at System Preferences > Network, Location - Automatic, Show built-in Ethernet: Good one has reasonable numbers for IP Address, Subnet Mask, and Router. Suspect has blanks. Each has AppleTalk active, reasonable values fo DHCP Client ID, and Ethernet Address, each is configured using DHCP.
I haven't cycled the power for the router, but I have for the hub. That made no difference.