Totally depends on the computer and the TV. My computer has HDMI out, and because I have an HD TV, I play almost all of my games that way. Chances are, if you have an HD TV, you'll totally be able to.
That's depending on the software specs you have on your computer. If you have the correct specs or better, than you won't waste your money. If not, then it'll be a waste.
It's not working for me on Windows 8. It keeps saying that I have a critical error with my detected configuration. No amount of tinkering with it seems to make a difference.
I remember being frustrated with the same issue. I think you can find it on the Steam website, but I don't remember where. You might access the steam community or ask tech support.