With limited RAM, instead of the Live-CD use the alternate desktop CD
to allow installation.

Go back to older versions for older computers and instead of Gnome or
KDE, use the less resource-intensive Xubuntu or Fluxbox desktops.

MEPIS 7 is KDE based upon Debian Stable and will run in such computers
as you described. Anti-X is MEPIS Debian Testing with Fluxbox and will
run with even less RAM.

And just in case you didn't know, this is the treasure-trove listing
of Linux releases.
http://distrowatch.com/