I have a Nvidia card with a DVI-to-HDMI adapter on it, and I had the same audio issues you're seeing. My understanding of it is that the card is spitting out audio packets along with the video packets. But since the graphics card doesn't have any audio on it, those packets are empty.
I've read numerous accounts of people connecting the SPDIF output on their mainboard to the SPDIF input on the graphics card and remedying the situation, but my mainboard doesn't have SPDIF capability.
So I fixed it by going into the Nvidia Control Panel and in the "Change Resolution" section, changing it to "HDMI - HDTV (Audio Disabled)".
This gets rid of those empty packets and my TV then begins listening to the analog audio inputs again.
The funny thing about it, though, is that it doesn't work after a reboot. It'll come up, and claim to still be in "Audio Disabled" mode, but no sound will come out. I've discovered through trial and error that I can change that setting to "HDMI - HDTV (Audio Enabled)", click Apply, and then say No to the prompt about keeping changes. On my particular setup, the screen then goes dark and I have to turn the TV off and on again, but when the TV reboots I'll have sound.
I think that's a major bug in the Nvidia software and I'm looking at installing a Radeon 4650 to bump the WAF up a bit, but it has solved my problem temporarily and might at least give you something to work with before getting a new card.
Also, here's a post on another forum that I found in my travels with a software approach. I never had a lot of luck with it though.