I once installed Slackware 7.1 on a Toshiba T1950CT (8MB RAM, 200MB HDD), so I think that may work for you too. Did not run X though, but I'd read on some page with installation notes that it is possible with old hardware like this (but very slow!). I used the floppy installation method. It took a long time, and I had to split some files for transfer, but it worked.
I hope that helps.