Maybe there's a better way to go about this. What I want to do is render 2 scenes for every frame and use the result from the first render as a texture in the next.
Scene 2: A room animated with a computer on the desk.
Scene 1: The screen of the computer.
This probably isn't even possible in the method I'm describing, but I think you'll see what I'm getting at. How can this be done in Blender Internal?