There could be all manner of reasons for this but since we don't know what your connection to the Internet is, you'll need to provide us with some more info:
What Country/State/Province do you live in?
Modem brand & model number:
Router brand & model number:
Network Connection Type: Wireless/Wired
If Wireless, what type of encryption are you using?
Things you have tried:
Is UPnP Enabled? Yes/no/Unknown
Is NAT Type Open?
Any Error Codes you encounter:
What type of internet do you have? Cable/DSL/T1/3G?
Who is your ISP(Internet Service Provider)?
When you run "Test Xbox LIVE connection" what is the exact message shown on screen?
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