I'm not very sure but you could try installing
Damn Small Linux, which you can
install from floppy discs (make sure you follow those instructions correctly!).
Then, for a one-floppy-disc distribution there are things like
FD Linux,
tomsrtbt, and
hal91. If you're looking for a slightly more security-related toolkit, then I suggest
Trinux. These are all text based distros, because they fit on one floppy. If you're looking for a graphical distro, then I suggest you try the Damn Small Linux link above, but I'm not really sure if it'll work on your laptop.....Have you tried searching Google for "linux floppy install"? Good luck!
[EDIT]
Don't think you can connect them via serial/parallel, but wouldn't it just be easier to have a hub and network both of them?
J_K9