Verify your security information. For example, verify the Phone number, Alternate email address, and Security question information.
Sign out of your Microsoft account, and then sign in again.
Try to sign in to Xbox Live again.
Solution 2: Clear the system cache
Press the Guide button on your controller.
Go to settings and select System Settings.
Select Storage or Memory.
Highlight any storage device, and then press Y on your controller. (It doesn't matter which storage device you select; the cache will be cleared for all storage devices.)
Select Clear System Cache.
When you’re prompted to confirm storage device maintenance, select Yes.
Restart your console.
Solution 3: Move and then redownload your Xbox Live profile
Note If you want to use a USB flash drive or a USB hard drive to complete these steps, you must format the USB flash drive or USB hard drive for Xbox storage. (See Xbox 360 USB flash drive support.)
Move your profile to a USB flash drive or USB hard drive. To do this, follow these steps:
Plug the USB drive into your console.
From the Dashboard, go to settings and select Storage.
Select All Devices.
Select Profiles, and then select your gamer profile.
Select the Memory Unit that you want to move your profile to.
Note A Memory Unit can be a USB flash drive, a USB hard drive, or the Xbox 360 Hard Drive. Be sure that you move the profile to a USB flash drive or a USB hard drive.