Well, I finally did it. I managed to get the new-upstairs-box running Elive/Debian to share its wireless internet connection to another computer via a wired NIC.
I tried using Firestarter with no luck. Its internet connection wizard wasn’t very wizardly. My guess is the script gets confuzzled by any NIC that isn’t ethX. I reckon some Linux geeks can’t imagine why anyone would one to have a box with wireless share the connection with another computer using a wired NIC. I reckon they must enjoy running a couple hundred feet of Cat 5e wire through the walls and floors of their homes so they can have a couple of boxes connected to the interwebs at the far end of the house.
I relied primarily on this and this for information. One warning, make sure that you have a dhcp server installed and that ip forwarding is enabled. I think that the Ubuntu forums assume anyone trying to share an internet connection would know to do that.
Update 2008/06/22: I had to uninstall Exalt, the E network manager, to maintain a persistent connection. For some damn reason, ever so often, Exalt would decide that the wired NIC was the default internet connection and hilarity (no working internet or sharing) would ensure. Using network-admin to restart the NICs temporarily overrode Exalt. Once I got rid of Exalt and rebooted (yes, I know; but I’m lazy), no more problems.