I tried run level 4 -- to give the graphic login a go -- and have a
problem that I can't seem to locate.

Logging in as root and selecting a KDE session I get logged in as I
expect. Logging in as anybody else (even though I select a KDE session)
I get a blank, Gnome-looking purple screen and can only get out of it
with Ctrl-Alt-Shift-Backspace.

Does anybody know what file needs to be edited so the thing will log in
and start KDE?

Thanks.