I would try <a href="http://tinfoilhat.shmoo.com/">Tinfoil Hat</a>. It has tools necessary for compilation (I'd imagine it has make included) but you might be stuck using cc/gcc and manually linking the files, which would be horrible.
Failing that, <a href="http://www.serverelements.com/">NASLite</a> is a floppy distro, but I don't know how suitable it is for building a system.
I guess since there are no ethernet ports and (I assume) no CD drive, that it doesn't have USB? If it does, is the BIOS new enough to boot from it? If you can you should definitely try <a href="http://www.damnsmalllinux.org/">Damn Small Linux</a>.
Probably what I'd do is cross-compile on another machine, preferably with the same architecture (then it's really just compiling, not cross-compiling) and transfer the data with a floppy. If you wanted to, you could take out the drive and compile directly onto it - that way you could set up your root FS tree in a GUI. You'd just need to make sure you either use the same kernel in the laptop as the compiling machine, or don't compile any modules and build a monolithic kernel on the laptop.