DSL should work, considering its required specs, but installing it will be problematic, so you'd better start with a plain Debian and use the install from hdd option (which many distros used to support, with some caveat, like RedHat needing the supplemental floppy but not supporting your PCMCIA floppy drive...)
The simplest solution would be to use ZipSlack, the last version based on Slackware 11 uses the kernel 2.4.33
http://slackware.cs.utah.edu/pub/slackware/sl … e-11.0/zipslack
Or Mulinux using the direct hdd install, but that one uses the 2.0.36 kernel, so it's very old
http://micheleandreoli.org/public/Software/mu … ux/mulinux.html
Both install directly to your FAT partition, so it's handy, as you don't have to deal with the unsupported PCMCIA floppy drive.
You can find some tips for your model on http://www.linux-on-laptops.com/toshiba.html