I bought a systemax system about a year ago. Model# SYXS-DB-989150.

I think the specs a

CPU: PENTIUM P4 3.06 (probably celeron)
MB: P4M800-M7A
RAM: 1GB

Anyway, after receiving my product, I attached two extra hard drives
immediately afterwards, and my troubles started a few weeks
afterwards. The hard drive which was attached as a slave to the C
drive would not show up from time to time when I booted my computer.
However, if I restarted it, it would appear, so I just lived with it.

Then sometime in January, my house had a blackout. After that,
whenever I did something that required a lot of data transfer from one
hard drive to another, the computer would just restart without
warning. I don't do games, but I do use a lot of video related
software such as AutoGK or DVD Shrink, and those are the only times
when the computer would restart. When using Office programs or
Firefox, the computer would run fine. I do however, have a suspicion
that Winamp caused the computer to crash quite a few times.
Looking around, I found that you could configure a setting in "My
Computer Advanced" where you could have a blue screen of
death appear instead of the computer simply resurrecting itself. I did
that, and no BSOD.
Then, I downloaded memtest and tested the ram with 5 passes. It passed
with flying colors.
I also downloaded SpeedFan to see whether the temperature ever went
ballistic while I was running DVD Shrink. I never managed to catch the
moment when the computer crashed but the temperature was always below
the 60 degree mark and only exceeded 50 sporadically.
Finally, I downloaded "CPU Burn-in" and let it rip. This
managed to crash my machine everytime, and I'm quite sure this fouled
up my computer for good. Now, it randomly reboots anytime it feels
like it.

So my question is: Is this a problem with my CPU, motherboard, or
both?

I'll just buy the parts and replace them myself, but I'd like to
salvage what I can rather than buying both parts (which would be a
surefire remedy but I might be throwing away a perfectly good CPU or
motherboard).