Instructions
Turn on the Xbox 360 and don't sign in to any profiles. If the console automatically signs in to another profile, press the "Guide" button, then press "X."
Press the "Guide" button after the console boots up to recall the "Home" tab of the "Guide" menu.
Choose "Recover Gamertag," then select "Recover Gamertag" again when a prompt appears introducing you to the gamertag recovery wizard.
Select "Yes" after the console informs you that it will sign into Xbox Live and load the gamertag recovery wizard.
Highlight the "Gamertag" text field, then press "A." An on-screen keyboard will appear. Type in your gamertag and press the "Start" button on your controller.
Select "Continue" to move on to the next gamertag recovery prompt.
Highlight the "Windows Live ID" text field, then press "A." Another on-screen keyboard will appear. Enter your Windows Live ID, then press the "Start" button.
Highlight the "Password" text field; press "A." Another on-screen keyboard will appear. Enter the Windows Live ID password, then press the "Start" button. A "Sign in" button will appear on the screen.
Select "Sign in." The console will take a few minutes to recover the gamertag and download all of its information to the new console.