Audio over DVI cable?

Its called a DVI to HDMI adapter.

Use ATI provided DVI/HDMI converter. You don't need to buy it. Call the video card vendor and they will send you one. Every card comes with DVI/HDMI converter and HDMI cable. Sometimes a note is provided on the box to call the vendor to request such item.

HDMI audio will only work if both ends are HDCP compliant. Not a problem for most people that have purchased an HDTV / monitor in the last few years, but still needs to be confirmed with your equipment.

http://en.wikipedia.org/wiki/HDMI#HDCP

I've got one PC to TV with a DVI to HDMI cord and I run the audio through the headphone slot to the TV, works fine. You just need a headphone splitter on your PC if you already use the hole for your screen audio. You'll then need a headphone extension cord of some sort - should be a black square hole on the rear of your TV for the headphone cord. I then have my tv joined to home theatre with a HDMI cord and that works fine...

I have an ATI card with two DVI ports and no HDMI. Using a DVI-HDMI cable to a TV, in Windows I get no audio (as is well reported on the internet, suggesting an ATI DVI-HDMI dongle is required) and the option to enable it is greyed out. However, in Linux, with the standard radeon driver, it quite happily provides audio to the TV.

This is clearly an ATI driver issue.