It is good that you increased to 64 MB RAM, I don't know how you can effectively run a big distro like Mandrake using X with any thing less. You can download Mandrake here:
The 9.2 download is about 5 GB, which includes a lot of applications (SAMBA Server, SSH, Mozilla Browser, GAIM Instant Messaging, a Flight Simulator, and hundreds more). I was not able on my Toshiba to get the CR-ROM recognized, so I opted for a network install. The Mandrake install did recognize my PCMCIA port as well as my 10/100 ethernet card, so a network install was feasible (FWIW, SuSE and Slackware 9.1 was able to recognize this as well).
Because I *only* had 64 MB RAM, Mandrake would not allow me to run FTP install, so I did it over NFS. I have another Linux Box with the full 5 GB distro that served as NFS server. If you do not have 5GB available for download on another Linux machine for NFS install (either as individual files or as .ISO files for CD-ROM installation or even if your CD-ROM is not recognized by the Linux install process) you may be able to do an http install, but I have never tried this.
In order to get this to work, I did a large root and swap (approx 850 and 260 MB respectively) partition and a correspondingly small home partition (approx 250 MB). This seemed to be the key to having Mandrake install as anything smaller on either the root or swap partition caused the install process to basically hang. I did a minimal install, with X and IceWM desktop and afterword loaded the other RPMS that I needed, Mozilla, SSHD, SAMBA, XVNC.
Mandrake is a relatively easy distro to install and for this they are known. I have it running on 3 boxes P4 w/256 mb ram, P1 200mmx w/128 mb ram, and P1 120 w/64 mb ram. All the machines are networked to my wife's P4 w/512 mb ram Win XP (she actually prints through SAMBA as the HP printer is on my P4 Linux box. Also on this P4 box is my HP SCSI scanner and Jaz Drive.
In fact I am typing this message while at work SSH tunneled into the P4 running XVNC.
The other "programs" mentioned (Knoppix, Damnsmall, SuSE, Slackware are all Linux distros).
Good luck and keep me posted. Hafl the fun with Linux is getting it up and running, the other half is enjoying its many fruits - the destination and the journey.