There are some small systems on http://leaf.sf.net/
(most of which are firewalls, but the ideas are fairly general) - they use very small compressed boot images, extracting them into a ramdisk.
Without looking at the system you're using I couldn't tell you how to boot it from the hard drive, but it is almost certainly possible. The Linux kernel doesn't generally come smaller than 180kb or so.
If you *really* want a tiny system then QNX has a microkernel which can be reduced to something like 9kb - it's not Linux but it's a Posix system and quite a few Linux programs will compile on it. If your laptop has a reasonable amount of hard drive space then a small distribution like a base Slackware installation should fit anyhow..
It's possible to boot from two floppies, one with a kernel, one with a root image. There is a kernel option which you should be able to find somewhere (sorry, I forgot) which tells it to prompt to insert another disk to load the root from (after which you can in fact remove both disks, they end up in ram).
Hope this helps,