You might want to run memtest86 on it first. Ubuntu should have a copy, and maybe Knoppix if the Ubuntu one break. You can download a bootable floppy too if the CDs just don't work.
http://www.memtest.org/#downiso
Looks like there's a version you can drop on a USB key if you can boot from it.
If you get an error, swap the DIMMs, and/or try them singly to see which module is bad. If it finds no problems, let it run overnight to stress-test the chips.
If you still find no problems, hit it with Prime95. If that runs fine for 5-10 minutes (a couple hours if you want to be certain), you can consider your CPU and RAM clean. I hear it's on the UBCD; I can't find a bootable version anywhere.
Prime95 was never meant to be a system test, but it somehow manages to heat up both the CPU and RAM to the point that it can sniff out even the slightest problem.
Strange you had so many problems with the CDs; I haven't had CD problems in years. Still have DVD problems tho.