As far as watching your computer output on the TV. It depends mostly on your computer. The fact that you are asking leads me to believe that your computer is probably not set up for it
Much easier to just send the $1.04 to the cable company in my opinion.
I understand it's the point of doing business with an unappreciative company, but there are hassles on both sides. Cable for the the most part works, as unappreciative as your provider may seem for your business.
You may quickly tire of waiting for picture, even more advertising and technical hassles if you are using the computer to watch programing. You will also need a very high-speed internet connection (which most likely comes from the cable company).