Welcome to the computer hope forums.
We may need a few things clarifying before we can help though. You say that your computer just stopped working one day but you were able to re-install Windows. Are you only experiencing problems when using the TV as a display?
Assuming for the moment that you have a desktop monitor that is working, does the TV appear in the screen resolution options (TV must be connected to pc)? Does the POST or BIOS splash image display on the TV when you boot up the computer.
[POST = Power On Self Test, in other words all those white words on a black background you see when you hit the on button]
[BIOS splash image is the usually the first thing the computer displays, usually represents the branding of the motherboard or PC]