I shut it down, led monitor is connected with dp port, keyboard mouse speakers are connectedAre you shutting it down or putting it to sleep/hibernate? What external connections are on the computer (HDMI, USB Devices, etc)?
Id check for shorts, i had this happen to me once when the power switch wiring had worn through the insulation on a sharp piece of the interior of my case and was intermittently shorting together, turning the PC on and off at random. Took me months to track that down, i tried new mobo's, CPU, PSU all for nothing, 5 cents in electrical tape fixed the issue.