I am having the same problem, but in my case, it occurs with a PC that has been working without problems for more than a year. The user was working and decided to restart the computer. Upon restarting, it showed a message like "the system is now resetting", then it turned off. Next time the PC was turned on, it didn't show anything on screen; when I opened the case, the case and CPU fans where on by 2 or 3 seconds, then off, and so on... I've unplugged and plugged back every single cable and memory module, with no results. The PC has not been moved, so we can suspect any part is loosened. What can it be?
PD: my mobo is also a Gigabyte GA-B85M-D3H, and my configuration is very basic: one 4GB RAM module, a 1TB Western Digital hdd, and an LG DVD drive.