http://forums.nvidia.com/index.php?showtopic=99932
As I understand the solution, you have to edit the registry to overwrite Nvidia's own drivers that are incorrectly adding an audio signal to the DVI port. The problem occurs when the HDTV picks up instruction from the Nvidia card that the DVI/HDMI cable is carrying a "silent audio" signal, consequently turning off the 3.5mm analog port on the TV's shared HDMI input.
The solution may seem a little daunting at first, but if you're smart enough to figure out why this problem is occurring, you should also be able to follow the somewhat technical instructions on the link above and get your setup working properly.