If you use a HDMI connection, it will carry both sound and picture. If you use a RGB (VGA) connector, it will carry picture only so you should have sound with the computer. I don't know what DVI does, but apparently that's the source of your problem.
Okay I have read many forums and can't find the answer. I use my PC monitor and want to keep the sound through my normal speakers. I have DVI connection on my graphics card with a HDMI converter on that goes to my TV, the quality isn't great but works but I have no sound! I have fiddled with the sound settings setting HDMI to default etc, tried different ports on PC, I also have a aux lead from PC to TV which connects to green aux PC audio, also tried the headphone jack. I use realtek HD audio manager. Been on TV settings not many options nothing worked, I have a Bush 26" HD flatscreen. Tried different HDMI ports on TV. Any help would be great thanks. Also went on device manager and went onto sound and hardware is up to date.