OK. After changing virtually any part came out, that the wire, that comes from the case into MB, and turns on the power (power switch) have some kind of strange problem and probably switch in the case it short, and randomly signalls into MB, that button uis pressed, when its not.
Now my system is staying in shut down mode correctly.
Bu I still have issues when boot the system after the shut down.
It shows the screen, that overclocking failed, resets all overclocking settings, and resets itsef few times.
Also, PC is unable to restore from hybernate / Sleep mode. I read that the new MBs have this issue though.