Thanks, reloadron.
I can see that 3 wires per computer would be fine. Tapping the 5 volt rail for the status LED would work perfectly until I wanted to expand my little project to the Hard Drive LED and any other status LEDs.
Having, say a 5 volt output, could be also used for external monitoring.
A nice way of doing this may be with the LAN cable except prehaps when the router/switch is not working, access over the phone or web, etc. This beyond my scope. I can build things if told how, that is about it. If you folks have an interest, have at it. should start a new thread, however.