Booting itself could be WoL enabled in BIOS, look in there and see if its enabled or disabled and signal is triggering it to boot on the LAN or power supply ripple or motherboard capacitor dying and causing ripple causing it to trigger soft power boot. Its probably Wake on LAN that is causing it to boot. I have had my one computer with WoL enabled turn itself on as for somehow the local network is triggering it. Disabling this in BIOS fixed my issue with WoL booting the system when shut off.