I have no idea if this is related, but I am having irritating random shutdown problems with my Gigabyte GA-MA78G-DS3H mobo. I managed to be looking at HWMON just before one of these shutdowns - it showed CPU temp around 40*C, and voltages were correct. No reason that I could see to cause a shutdown. I have already tried a different PSU that successfully powers another system, and saw no improvement. I know that a number of others have had problems with the GA-MA78G-DS3H mobo - what about yours? I am about ready to give up on this POS. . .
I have Crucial Ballistix DDR2-800 2 x 1GB in this system, and I am beginning to suspect them as well. Unfortunately, I couldn't run memtest86 - when I tried, I got a never-ending stream of CPU register information. At the moment, I am trying to figure out why memtest86 isn't working properly.
FWIW, I just replaced some failed Ballistix in another system with Corsair Dominator DDR2-1066, and couldn't be happier. Clearly, Crucial has had problems with their Ballistix line. You might try other RAM and see if that makes any difference.