Don't be fooled by the fact that your computer's graphics board and I/O board both hook up to things that look approximately ? um ? "screeny." They're totally different.
Sometimes, depending on the board in question, it's possible to pull a chunk of graphics memory back off the graphics card and run it through the necessary signal processing to turn it into a television signal. This is not all that common a feature, for the obvious reason that computer screens are computer screens and televisions are televisions, and they're not meant for the same things. To find out whether your board has a feature like this, check the manual. I know that a Kona board
may have the feature, depending on what version of the driver you have installed. (If I remember correctly, Aja pulled the feature from some driver releases because it wasn't working correctly. I don't think anybody actually noticed.)