It looks to me like your explorer.exe is corrupted. Even if it's a display issue, you should still see the taskbar at the bottom
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I don't know about Windows 8, but in all other Windows the taskbar does not extend to additional displays. I think what hosler is implying is that he has set his main display to the external port?
Either way, it's a very easy thing to check for. Fn+display key on the laptop will toggle through the external display settings.
It's worth at least checking into.