OT: system shuts off sporadically

[Vaughn Treude]

Hello everyone:
I've been experiencing a problem with one of my PC's.  Eight months ago
I upgraded it to an Abit VIA KM400A motherboard with an AMD processor
and new RAM.  In the last couple of weeks it's started shutting itself
off sporadically, for no apparent or consistent reason.  I know it's not
a software problem (though if anyone wonders, I've got Ubuntu on it, and
have been quite happy with that flavor of Linux) because it has at times
shut itself off while I'm in the BIOS setup screen.  I have replaced the
power supply and that didn't help.  I suppose it's probably a
motherboard problem, and I believe it's still under warranty, BUT
sending it back will be a hassle and I'll lose the use of that machine
for a few weeks at least. Most odiously, I'll have to reinstall the
processor and mess with that heat sink junk once again. So I'm wondering
if anybody knows of anything else that could cause this problem.

Some more info:
- The problem appears to be totally random, sometimes happening within a
minute of startup, sometimes hours later.
- Sometimes the system will not restart for a few minutes after this
happens.  Or sometimes it will start but not boot.
- Often when this happens the BIOS checksum gets corrupted and I have to
re-enter my settings.
- In BIOS, I've taken care to turn off features I'm not using, such as
APIC and SATA support. I've turned off power management to the extent
the BIOS allowed me to do that. I've also set the power-off switch mode
to a 4 second delay, in case there could be noise spikes on the power
switch line.  I've turned off the "halt on errors" feature.
- In the BIOS PC health screen the CPU temperature appears to be well
within the good range.  However, I've only checked this shortly after
power-on.
- The motherboard is rather compact, and is mounted in a maxi-tower case
with extra fans.  I don't know for a fact if the airflow is optimal.
- I've checked the system logs and there is absolutely no record of any
kind of error at the time it powers itself off.

Any ideas of what I might try, or any resources I could use?  I googled
for it under "PC sporadic shut off" but didn't get any useful hits. 
Half of the problem with googling for a PC problem is knowing what to
call it!

Thanks in advance for any suggestions you might have,
Vaughn