Sound like the system is restarting for lack of power or for some grounding issue.
Let’s try some basic Troubleshooting:
1) Try the system outside of the case to narrow any grounding problem. Carefully, try to turn the system making a jump (you can use a clip, keys or flat screwdriver) on the 2 red pins form the front panel header, this way we can determine if there is a problem on the front panel of the chassis.
2) Clear CMOS: removing the CMOS battery form the board for 5 minutes, after than unplug the power, then put it back in the same position, plug the power and give it a try.
3) Tested the system with basic configuration (only one memory stick on the blue DIMM closer to the processor) and with the BIOS jumper in maintenance mode. Just move the BIOS jumper one pin over. Please check the next link for more information: page 51, figure 27 (configuration mode) http://downloadmirror.intel.com/18702/eng/DH57JG_TechProdSpec.pdf
I do not know why, but now it turns on, but with network not working 5 of out of 6 times (as it has done earlier).
Maybe it depends on, if the PC have been turned off, but still with power supplied (when off but with power supplied, a green LED is lit on motherboard).
I think the motherboard is defective. If it was the CPU I guess the fault would be constant.
Thanks for your hint and link.