You are wrong in thinking you can get sound through DVI, which you cannot.
You will need to use your stereo audio out to pass audio to your TV. If you have optical out you can use that instead for digital audio as opposed to analog stereo audio.
There is also the following possible alternative to using your mini-DVI as the video out.
Note, if you are not using your TV all the time as a second monitor to your imac I recommend using SwitchResX. Then you can configure it to enable/disable the TV without having to connect and disconnect the cables or fiddling with system preferences to switch video and audio configurations. Once configured you can do the switching back and forth just by using a menu or a hot key.