You are going to have issues with that laptop, doesnt matter which linux you use, it can be done, but it will be work.
Slackware 3.5 can be installed via floppy, dunno if the stuff you need is available anymore or not, I think it is.
ftp://ftp.slackware.com/pub/slackware/slackware-3.5/
Ya its there.You will need a bootdisk, and root disk and a working computer to make them with.
You will also need from the slackware directory at that site the A,L,N directories---->once youve got those installed the rest will be easier.Get the K and D directories too, so you can compile stuff and have a kernel to work with.
Some notes, read the documentation carfeully, the kernel used wont support modern browsers like firefox for example or some of the newer software.Pick your kernel carefully, that laptop may have specific needs.Drivers for a pcmia NIC card or modem may be tough to find or get working, just warning you.
slackware uses a package system with NO dependency checking, check the docs for each major piece of software to make sure youve got what it needs installed.The L directory is all the libraries, its pretty inclusive but your bound to run into something you need that isnt there.
Oh ya, get some of the stuff from the ap directory, and make sure youve got the program called "pine" it comes with a very good editor called "pico", it will make your life easier.