My laptop has been running XP Media Center 2005 fine until today. It's permanently connected to a plasma screen via S-Video to Scart.
I can display the desktop, and anything else on the plasma, but now, when I start up Media Center, I just get a black screen on both the laptop and the plasma.
However, if I click on the Start button (on the keyboard) everything shows again until a click the pointer on the Media Center screen. Just goes black again with a white pointer in the middle of the screen for a few seconds.
If I take Media Center out of full screen mode, I can see it together with a taskbar.
Im not sure about how it works with your graphics card but usually with my pc which is also connected to a tv through an ATI Radeon graphics cards S-Video and you may have tried it - right click on your desktop then click propeties it should take you to display settings
Then press the settings tab and then advanced - with my graphics card there is a display showing overlay and then clone mode and then its set on same on all - this show the boot up and windows start up/login and explorer on my TV.
I think that should work. Otherwise backup your computer then try a driver rollback if this never occured before.