I had a ancient laptop like that once. A 386 I beleive... 
Not sure, it had a optional MMU upgrade for it, but I couldn't find a chip to stick in there.
I got linux installed on it once, but the lack of memory was the real killer. When you get under 8megs of RAM things start getting interesting. Around 4megs is very interesting.
You see most linux floppies don't actually run off of the floppy, they load a compressed image (in it's decompressed form) into RAM. So you end up having to have enough RAM to run the OS + hold the OS in a RAM disk.
So if you don't have enough RAM to do this then it gets difficult. Plus it had no networking capabilities to speak of so that every file I needed to transfer onto the disk had to go thru floppies, and that was fairly difficult and time consuming. Especially since my floppies are ancient and spent as much time on the floor as they do in the desk.
So eventually what I did was install a old version of DOS (6.00 not 6.22) and setup ppp over a null modem cable to my desktop and used kermit as a vt100 terminal for my desktop. It was very good for that, and I recommend that very much for anybody that has a old laptop.
However the ghosting on the ancient LCD display (only black and white btw) got to me and gave me I strain. So I installed some old dos games on it and gave it to my siblings as a curiousity/toy.
That is a nice thing though if you have a bunch of headless Linux servers. You can setup Lilo (and maybe grub) to run the main console/bootup screen thru a serial based tty, and thus be able to lock down your machine and still have it accessable thru a null modem serial cable (also called laplink for a popular commercial product that sold null modem cables as file transfer devices to and from your Win9x machines.)