Most NVidia video cards which support TV output are capable of routing any "full screen" video to the TV out. What this *actually* means is that if a video source is playing anywhere on the desktop, it will be enlarged and shown full-screen on the TV output, leaving the video in a window on the windows desktop.
I use this feature to watch DVDs (or I did, until I got a DVD player... I'm a poor student 😞 ). All you have to do is use a video player which supports hardware overlay. Just about any video player should support this either by default or with a setting inside the player. Windows Media Player does it by default. The full-screen output is configured using the "Advanced..." setting under the Display Control Panel -> Settings tab. It might take a little toying to figure it out at first, but I think this should serve your purposes quite well.
You can probably find an NVidia video card with TV out for US$50 or so if you look at some online merchants. The drivers are really just amazing in terms of what it lets you configure.
Good luck,
Dave