After looking around the 'net (Google is your friend...) I found a bit of information that I'd been overlooking and went to see if that would help me with getting DeLi to do what I wanted.
Fifth lesson: /dev/tty0 is not at all the same as /dev/ttyS0 - and /dev/ttyS0 is where the trackball was. But /dev/tty0 was what delisetup seemed to show. The install guide is right, but I misread it too many times, dagnabbit.
Sixth lesson: SuperProbe, like Google, is your friend. It told me what the video card was without any fiddling around. With that information (and the right trackball port!), delisetup could be told how to set up X.
And with
jmaynard's help:
Seventh lesson: DeLi thinks .xinitrc is only for root, it seems. A copy is needed in the user's directory ( /home/username ) for DeLi. Without that, startx throws you to the annoyingly primitive twm as the window manager. With a local copy of .xinitrc Icewm is used if selected - and it should be since DeLi is set to have all the menus right only for Icewm and not for any of the other window managers.
Eighth lesson: /etc/resolv.conf had to be made 'by hand' so that DeLi sees the domain it lives in and can also find the DNS.
Once all that was done, it began to act like I've come to expect a computer to act.
I don't have an IRC client installed - yet. That shouldn't be too hard to rectify. DeLi uses Slackware 7.1 packages, such as they are. I also still want to get sshd going. It's there, it just isn't happy and running yet.
I'm still a ways from really feeling I know it, but I'm feeling better about things. DeLi with Icewm is actually fairly snappy on a 90 MHz Pentium. With me logged in and running Icewm and Dillo (web browser) top showed that the system was getting a bit of a workout but wasn't straining. It wasn't touching swap at all and breton has only 32M RAM. Maybe if I'd been using graphical stuff more aggressively... but overall I'm impressed. I think with a bit more experience I wouldn't mind having a shot at putting DeLi on an older (and therefore cheaper) laptop.