It was the kernel. I'm running 2.4.1 now and that fixed it.
After I got the system into a known working state (by re-installing from
the unofficial Woody CDs) I built a new kernel. I figured out that I
have a problem with building 2.2.18pre21 now; I used to be able to build
it but no longer can. I built 2.4.1 instead, and net started working
perfectly. The version of tulip.c in the 2.4.1 kernel sources is new
enough to properly talk to my Linksys LNE100TX.
The USB howto file, version 0.8, contains advice that did NOT work for
me! I found a different howto file, and the advice in that file did
help me. The file that helped me was here:
http://linuxkb.cheek.com/pages/usb-howto/book1.html
The command that made a working mouse device for me was:
mknod /dev/input/mice c 13 63
The 0.8 howto has a different command (mknod /dev/usbmouse0 c 180 16)
and that did NOT work for me. I believe the numbers "13 63" are correct
for my USB mouse; "180 16" didn't do anything for me.
By the way, I am loving 2.4.1; it built with no problems, my net card
worked without patching, and my system actually seems faster. I didn't
expect the system to really feel faster, but it does. Specifically,
Gnome starts up faster than before; that's where I really notice it.