The simple edit of /etc/network/interfaces did the trick.

Strangely, the first five or six times I booted into Knoppix without access to the network X windows would try to use an incorrect video configuration which resulted in nothing but video noise. A reboot would bring me back into a correct X-Windows video config. I haven't had this problem for a couple days, perhaps some upgrades changed something--I can't be sure.

All is well at the moment. Now I'm trying to get Knoppix into my dad's gateway desktop. It's not handling the P4 or the flat panel correctly... we'll get it figured out. I'm firmly convinced that Knoppix makes a great Debian installer.