I have successfully installed RedHat 6.2 with CLE 0.9p1 (Chinese Language Extension) on a second partition on my Vaio C1VJ. It was tricky, first of all I don't have the USB floppy drive, and the bootable CD-ROM drive will boot the installation CD, but during installation, it will not detect the drive as valid. So what I ended up doing is to go back to Win ME, copy all files from RedHat 6.2 CD to HDD,
and then during installation, I have to specify the directory on /dev/hda1 containing the installation file.
After intallation, lilo would not boot, it turned out the version included with 6.2 have trouble with first partition over 2GB, so I went back to Win ME, used Partition Magic to move the windows partition to the end of the drive and installed linux onto the partition in the front.
After that its just to get the X Server to work, someone already have a patched ATI Mach64 server for that funky 1024x480 resolution, and the Jog Dial server, although I have not find any application that uses it. They can be found here:
http://www05.u-page.so-net.ne.jp/tc4/t-kinjo/vaio/index.html
the instructions on how to install are for some japanese linux distribution, so its different than redhat 6.2, and I don't remember what I did to get all the links to point to the correct location.
Also I have not tried to compile the kernel on it.
It uses the ATI Rage Mobility-M1 chip with 8MB on chip video RAM.