Make sure the connection from the graphics card to the LCD is done by using the supplied DVI-to-HDMI adapter that came with the card, and obviously also with a HDMI cable.
Assuming all the drivers are correctly installed, go into the Sound and Audio Devices area in the Control Panel in Windows, and then change the default sound device to the ATi HD one (Note that this is for Windows XP, otherwise Vista would be different but still easy to see). Test it by playing the Windows sound effects or something to see if you hear anything coming out from the LCD TV's speakers.
If this works, make sure that any Media Player programs have selected the ATi HD sound option too.