Take a look at the Xbox Support pages below, they might help you solve your issue.
- Troubleshoot Your Xbox Live Connection
- According to your problem description, item "Xbox Live" is not connecting:
This test verifies that your Xbox 360 console can contact Xbox Live. If your console does not pass this test, check your results for these other connection tests:
A failure on any of these tests will prevent you from signing in to Xbox Live. If your console passes all of these tests and still cannot contact Xbox Live, verify that your account information is accurate and up to date.
- According to your problem description, item "Xbox Live" is not connecting:
{One of my posts at "Xbox Live香港(Hong Kong)討論區" dated "04-22-2008, 07:27AM"}