It's certainly possible; most distros have alternate install methods that are documented on either their install CDs or web-site.
First of all, be careful when choosing a distribution. Most modern distros will want a minimum of an i586 or i686 (Pentium or above) in order to run. You will probably be best off looking for a dedicated web/ftp distro on www.distrowatch.org
You will have to partition your hard disk first if you want to install from the hard disk. The easiest way to do that is to download the bootable floppy version of gnuparted from http://www.gnu.org/software/parted/#downloading
(see the boot disk image in /gnu/parted/bootdisk)
To take one example, the drinou distro (http://distrowatch.com/table.php?distribution=drinou
) fits your requirements, and can be installed from disk (although the site was down when I checked).