Xbox 360 turned off while updating
And further, that my system started exhibiting bizarre menu lag for no apparent reason.
When it finally happened, it was without notification.
Following weeks of wall-to-wall, often sleepless gaming, I finally parked my Xbox One in an armoire in my living room, dropped the gamepad in a drawer and took a much-needed break.
I needed some downtime from the console’s beautiful rides and zombie mobs and risible breast physics.
I've noticed that the 360 won't boot up unless the HDMI finishes a handshake with the TV first.
Can you try with a different HDMI cable or with an RCA or Component Video and see if that has the same effect? Update: I've traded up for a 320GB Slim, it is the same situation.