Ramon’s tips helped me a bit further, because they enabled me to test some of the settings and try where the problem is.

I now encounter a very nice but weird phenomenon: when I use DualView on my NVidia card, I can drag Media Center to my TV. This works and shows up properly. When I maximize Media Center the image is all garbled up. But: when I open another window (this can be anything: notepad, display properties or the DirectX Control Panel (By the way: thanks for that one Ramon!)) and give this other window the focus, my Media Center display perfect. As soon as Media Center gets the focus, its image garbles up.

So: when it doesn’t have focus, it displays properly but I can’t use it. When it has focus, I can use it, but I can’t see what I’m doing… Nice.
I’l keep on going till this thing works!