My xbox 360 froze while updating
Xbox One supports HDMI CEC standard, which is enabled by default (as opposed to PS4 where it seems off by default afaik).
If you have a newer TV which also supports this feature, and the XBox is connected using HDMI then it may be turning on whenever you turn on the TV.
Choose "Install Game" and then wait while the information is downloaded.
With the disc still in the tray, try playing again. If your disc has been severely scratched or scuffed, it could cause your game to freeze up.
Also make sure that the Xbox 360 is not on carpet or any other soft surface, as this will clog ventilation. With larger games like Star Ocean or the Last Remnant, your Xbox 360 can overload when reading the massive amount of data coming from the disk.
Download the game to your hard drive by putting the disc in the tray and then pressing Y at the game's frame on the Xbox 360 dashboard.
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I've experienced something very similar with my Windows 10 PC turning itself on to download an update (but not install it until I manually restart). Since the console doesn't have a physical power button, certain things falling/resting in front of the button may trigger it.
If this persists, I'd contact Microsoft as you may have some sort of a connection problem with the power button.
I have had this happen to me many times now, I think it may have started when I connected some external HDDs to my Xbox for additional storage.
hahahha I got so excited when I saw how many post there were, figured I may have a fix on my hands. I hope it works itself out, I would'nt tell them that you did anything though, I'd say it just stopped working and get it replaced, it sucks but that way you know it will be fixed.
But then again, some classic GB trolling to work me back in wasn't half bad either. Haven't been able to get a system update to work off of a flashdrive yet though.