I'm not familiar with your motherboard, but I am familiar with your problem. Some network drivers have default settings where the wired or wireless network adapter can "wake" or "start" the computer. On my laptop when I first came across this problem, the BIOS was not set with the network device in the boot devices list. Don't quote me, but I believe the adapter's default settings and the BIOS boot devices settings are two independent and separate things.
In my LAN, if one computer is connected and running, and any other is set to wake on magic packet, it will restart on its own. I'm using Windows, and the operating system scans the local network at regular intervals to detect newly connected or disconnected devices. It seems that the scan wakes up the laptop, but then again, a video game console configured to connect to a media server might also do it. I'm still trying to understand exactly why it happens, since I would like to boot and access a computer remotely, but it's not a high priority at the moment.
Check your network adapter's settings, and see if it is set to wake on magic packet, pattern, or both. If it is, disable this setting, save, exit, and then shutdown your computer. If it stays off, you've found your problem.