Model number of your TV would help a lot, as we can determine what connection types the TV has, as well as resolution options (you mentioned 720p in title of thread).
Also, specs on your desktop computer would be great. Specifically, information on your GPU (graphics processing unit or video card). This will help us understand what it's capable of, and what video outputs it has. We don't know if you're using a very ancient computer, or a modern one with an HDMI output, or just a DVI output, etc. Hopefully you get the point.