Well these forums are really about programming using DirectX (on windows) or XNA Game Studio (windows or 360) so you are a little off topic.
There is no way any of the technologies we cover here can do what you want. XNA GS cannot access the internet and writing a web browser would be a huge task for anyone to do on their own.
Really your best bet is to buy a cheap PC and put it under your TV. If you get a more powerful one you could also run Media Center on it.
If you insist on going through your xbox 360 then the xbox or media center forums would be much better places to ask. Maybe there is a workaround to the pop up problem.
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