You should let us know which TV and Graphic card you are using, the resolution settings and possibly any other computer parts that may help us answer your question.
I've plugged my computer via a DVI to HDMI converter, and a high quality HDMI cable to a SOny Bravia S series, 1080p, in order to test the theory. Perfect image. But then I bought a Sharp Aquos 1080p once I was confident that it was a good move, but the image was terrible compared to my monitor. I did a lot of tampering with the TV settings and finally got it up to par with the monitor a couple of days later.
Here are some smalls tips I can begin with for now. First make sure the TV itself is running the image pixel per pixel and not in any zoom mode or automatic cropping modes. Make sure you video card can output a digital 1920x1080 resolution or greater. If so, put the resolution in 1920x1080 mode (if your TV is 1080p that is), make sure your video card drivers are updated as well.
Can you describe to us what was wrong with the picture? Colours, size, distortion, static?