Situation: Bought a new big LCD TV with HDMI input. Got an year-old HTPC with Athlon 64 X2, Gigabyte motherboard and ATI Radeon HD 3200 integrated graphics. HTPC has a HDMI output. Connect it up with the LCD TV, but only gets video (Windows Vista desktop in 1920x1080 glory on a 55" LCD TV). No sound what so ever.
Going into Control Panel to change the audio playback device, and saw that "ATI HDMI Output" device showing "Not plugged in", and unable to be selected.
Solution: I googled the problem, browsed a few solutions in various forums, opened up the HTPC case to make sure everything is plugged in properly (which they are, as it's actually an all-in-one motherboard), updated to the latest ATI driver, etc. Nope. Nothing works.
Then it turns out that it's just a matter of getting into the BIOS (pressing [DEL] when the computer boots), going into "Advanced BIOS feature", and changing "Onboard VGA Output Connect" to "D-SUB/HDMI". It is usually "D-SUB/DVI" as default setting.
Booting back into Windows, and the audio would just work :)