DVI and HDMI are Both Digital

Not only are DVI and HDMI both digital video signals, they are the same video signal. The only difference between HDMI and DVI is that DVI was intended for computer monitors so no sound is included, where HDMI was intended to be used with TVs, so audio is integrated. Connecting the DVI port on your computer to the HDMI port on your HDTV will give you the best video quality possible.

DVI to HDMI Flat Cable, 6 ft.
$24.26

DVI to HDMI Method #1: Simple Cables

So, since DVI is the same as HDMI but without the audio, you can use a simple cable to connect your DVI computer to your HDMI TV to handle the video, and a seperate audio cable to go from your computer's 3.5mm stereo audio port to your TV's dual stereo audio RCA ports. This is probably the cheapest way to connect a DVI computer to an HDMI TV.

Vantora DVI + S/PDIF to HDMI Converter and HDMI Splitter
$49.95

DVI to HDMI Method #2: Conversion Box

This box allows you to plug in both a DVI source and also an audio source, integrated the video and audio together at the box, outputing HDMI with integrated audio. Although this option is a bit more expensive, it gives you two big advantages. For not that much more money, the conversion box allows you to integrate digital audio (coax or optical) in with your HDMI signal giving you the ability to achieve 8 channel surround sound if desired (the first option above only allows stereo audio with the seperate audio cable). The second great advantage is the reduction of cable clutter when using a conversion box.