Look at my post, your problem is the thermal paste of your power brick transistors!

If your xbox is turning off randomly (mostly after turning it on)... and its related to the power supply : if you unplug the power supply, wait a few min and you plug it back on and it is back to working conditions just to turn off after you try to launch a game...

Well then the issue is the thermal paste of the transistors of your power supply.

Open your power supply, unscrew the transistors, clean the old thermal paste, put new thermal paste, screw them back in.

DONE! Solved my problem, now xbox not shutting down by it self...