I've built 20 systems on this motherboard, and some users complain that sometimes they find their computer switched on the next morning. Obviously after they shutdown their computer restarts.
From a brief investigation I did, it appears they restart randomly - even after hours that they shutdown.
I am guessing we have a similar problem. I would exclude the power supply as my systems have various power supplies.
My setup is similar:
Win XP Sp3
Athlon 64 X2 5000+ Black
Gigabyte GA-MA78GM-S2H (Bios Version F3)
Kingston 2x1GB 1066MHz
Various power supplies
You did not mention your OS, but comparing our setups, it appears that excluding the motherboard we have at least 1 more thing common - the memory type. However since you are on phenom, your memory runs at 1066MHz while mine is running at 800Mhz.
What bios version are you on?