I've had lots of experience with this error message on many computers, and I don't think it can really be blamed on AMD or VIA. I took apart and rebuilt about 40 older pentium systems and had this problem pop up quite often. Power issues could definitely be causing it, like someone else just said... (the power supplies on these machines were quite prone to sudden death.
However, to me it seems more like a memory issue. Not necessarily bad memory sticks, but possibly wrong settings. I've gotten the errors to go away (some of the time anyway) by changing the memory settings (timing, etc) and moving the sticks around. Messing with other settings in BIOS has worked for me as well.
One thing I have noticed is that when I have a computer thats getting those "machine check: regs" errors, windows seems to slowly but gradually get corrupted and almost always needs to be reformatted, although it can take months to a year before it gets that bad. This is what leads me to believe it could be a memory related error message... even if your memory sticks pass memtest etc, maybe they just don't work well with your particular motherboard?
Just my thoughts,
Peace