No "real" (I.E. a full distribution) can be installed only from floppies anymore, the typical install is now much much too large for that. It would take thousands of floppy disks to fit everything.
Your best bet is to use something like Debian or even OpenBSD which allows you to start a network (Internet) install from floppies. You don't mention any network device currently, but getting a cheap PCMCIA Ethernet adapter would work.
Alternately you could pull the drive from the laptop and put the installation files onto it, then install from that (boot to floppy and point the installer at the HDD for the source), but I don't think you will have the space for that on only 2 GB (the 12 GB drive would be enough though).
Personally I would go with the single-floppy network install of OpenBSD, as I have just had better luck with BSD on machines of that era. I don't like running Linux on anything much lower than 200 MHz, as it just doesn't feel like the performance is at an acceptable level to me.
Last edited by MS3FGX; 06-04-2008 at 02:41 PM.