My XBOX's dashboard/firmware was from sometime in 2008 when I first bought the system.  I mainly played using composite cables but at my brother in law's house we used HDMI.  The very first time it worked, but then I bought some games that did some update and after that HDMI never worked.

The symptoms besides having on sound is that your XBOX will show PC monitor resolutions but won't have any option to say you have a 720P or 1080P display, this means the XBOX firmware is faulty/defective because it can't recognize that you have an HDMI cable plugged in.

This happened on two different TV's with different cables, I tried the unplugging the cable and plugging it back in trick and powering/on off the TV and XBOX etc... I have no idea why anyone suggested that because it never worked for me in any case.

The problem is that your dashboard is out of date and is buggy/defective.

The Right Trigger/Y Startup Trick Did not Help

I tried all the tricks such as the "holding the right trigger and Y trick" during startup.

There was no Disable Display Discovery or Disable Display Detction in my Options/Dashboard/Display

That's when I decided to update my dashboard, after that my HDMI sound worked because the XBOX 360 finally realized I had an HDMI cable plugged in .  I did however have to Disable Display Discovery or whatever it is called (you finally get that option once you update the dashboard).

Click here to download the latest firmware (don't worry if you don't have an XBOX HDD, it will at least update the dashboard before saying that you don't have enough space to install the upate).

I used my USB drive to download the update, here is the link from Microsoft to download it: http://download.microsoft.com/download/1/d/8/1d8c09be-278e-41cd-98be-eb9188128227/$systemupdate9199.zip

After that sound over HDMI will work with your XBOX 360.