Given the age of your Xbox 360, you will not have an HDMI port. Prior to the new Xbox 360 slim version, only the Xbox 360 Elite version had an HDMI port. It is easy to identify as it was the Xbox 360 that was solid black, with no extra graphics.
You can still get HD-quality output from your 360 by connecting to you HD-capable tv with component cables. They are a set of three cables where the cable ends are blue, green, and red for video. Then for sound you have the option of the red and white audio cables, which will give you stereo audio output, or to get surround sound, if the game supports it, you use an optical cable (fiber optic) connected to the small square-ish hole, the looks like someone knocked two corners off. The component video cables, with the optical audio cable will provide as good an HD experience as HDMI would have.
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