Q: Mac OS X doesn't detect TV as audio output device with HDMI

I recently bought a new TV and am trying to connect it to my Mac OS X 10.6.8 with a HDMI cord for the first time. I have perfect video but there is no audio. I realize there have been about a billion threads with the same problem, and I assure you I've read so, SO MANY of them. The problem is that when I go to System Preferences > Sound > Sound Effects, I cannot choose my TV from "Play sound effects through" because it is not listed. "Internal speakers" is the only option. Same thing goes when I click on the "Output" tab (no TV is listed; only Internal Speakers), when I click Option + the Speaker icon, and even in Audio MIDI Setup. My Mac doesn't seem to detect my TV as an audio output device anywhere.

At this point, I'm wondering if it's the TV. The TV is a Westinghouse DW37H1G1, and there is a tiny line in the user manual that says "When HDMI has an input signal coming from a DVI source then the audio input signal must be connected to the PC audio input." Now, both the HDMI cable and the adapter specifically said they support both audio and video. But does the phrase I just copied--which I can't decipher--mean I have to buy another effing cord? If so, what is this other freaking cord I have to buy that will go between my Mac OS X 10.6.8 and the PC Audio spot on my TV?

Or--hopefully--there is something else I need to do with the configurations of my Mac so that it will get audio to the TV.

All help is appreciated. Please know that I study 17th century rhetoric, so if you could dumb down the techie lingo for me, I'd be most thankful.