Caught at one hundred and twenty metres per second

The picture below is a hardware test setup I ran this morning, with an old and discarded motherboard which has a Pentium III CPU on it running at 733 MHz. Since that's still faster than any other system I own save for the ibook (which is a G3 running at 800 MHz), I wanted to see if it was truely broken as reported, or not. The issue, which I actually witnessed before, was that on initial boot it tended to restart up, to a few dozen times. These restarts could happen from early post BIOS stage up to while logging on. Once it had been powered on for a little while, the restarts would usually go away.



I assembled any missing parts - video card, memory, and an AT case from which I used the reset button as the power switch to the ATX motherboard - and started by running memtest on it. Which ran just fine for nearly half an hour; but I ran memtest before to try and help diagnose the problem and it had run fine then, too.
So I crossed my fingers and tried running a Linux Live CD from it. Unfortunately, after about half a minute the system restarted once again. The only parts remaining from the original system were the motherboard and CPU, power supply and DVD-ROM (but not the IDE cable). With that in mind, the most likely culprits are indeed motherboard or CPU.

Chances of being able to rescue the parts are nearly nil, but I'm still curious about what could be the actual failing part. Are there any thorough hardware tests around, which could be run (preferably) from bootable CD or floppy?