So recently today I turned on my Xbox 360, to my dismay, I kept hanging upon startup. If this problem has been happening to you as well, then just follow these steps.
1) Turn off your Xbox.
2) Plug out your ethernet cable ( for those using wireless I'm not sure about you guys, sorry :/ )
3) Turn on your Xbox, after the Xbox 360 logo appears and the gray screen appears, click your Home Button and launch the disc inside immediately. ( Do not wait for the Xbox to sign into your profile )
4) Once the game has launched or to be safe, goes to the start screen, plug in your ethernet cable and connect to Xbox live.
5) Kick ***!
If these steps do not work, I am sorry, this method has been working for me and my friends.