This problem seems pretty popular. From what I can find, most of the problems like this, when they are NOT due from BIOS settings, are caused by:
Keyboards and mice
Motherboard battery
PSU
Modems or other ethernet or phone line cable links
You can start canceling some of these things off the list, (unplug all ethernet cables and phone lines)(try other key board and mice, or {if none are available} try shutting down with the mouse alone {keyboard unplugged} or the keyboard alone {mouse unplugged, Press windows logo and navigate with arrow keys}, try another power supply, or replace motherboard battery. The battery is cheap, but the power supply may not be.)
Some programs can also cause wake up after shutdown, but this is very rare.