I know that there are many gnu/linux distributions which can no longer even be installed on very old computers because of their size and/or distribution method; can you recommend any of the 100% free distributions for this purpose?
Depends on how you define "old". On a 10 year old system (say, a Pentium II with 128 mb of ram) you can easily run the current version of Debian even with the not bad-looking LXDE gui.
Gentoo Linux should also be able to run on pretty old machines (but I think it woud be a pain in the a** to compile it)
DSL (damn small linux) is also aimed at very old computers, I don't know, however, if it's 100% free.
In general it might be worthwhile to take a look at distributions for embedded linux, they often have clever solutions when it comes to limited resources.
Michael