I have the Dell Desktop XPS 8500 and got a slighter older LG TV. It has every connection under the sun except HDMI, so I used DVI to connect them. However, I found that there is no sound. So I got an RCA cable, Y Cable, and plugged into both the green plug on the back of the Dell and tried the speaker plug as well, to no avail.
Let's backup. The XPS 8500 is on. The TV is on and you can see the Windows Desktop on the TV. Insert a music CD into the XPS 8500 optical drive. It should start playing. Now, connect headphones into the rear green audio out jack. Do you hear the music on the headphones? - If yes, then the XPS 8500 audio is working and the culprit is how you are sending the audio into the TV - If no, then the XPS 8500 chipset and audio drivers should be reinstalled, then the system rebooted