The 3870 has a built in sound card. You would want to disable either the motherboards built in sound or if you have a add on sound card it needs to be disabled.
I run a hdmi out adapter from my 3870 to my receiver and then to the tv, though if you don't have a receiver or don't want to run it through one if you go straight to the tv the sound will work.
It could be that the dual d**k is the issue. My card has dual link but I only run out through one of the dvi connectors and use 1 hdmi adapter. Unless you are running at a resolution above 1920x1080 (or 1200) you do not need to go dual link. I would assume a 37" lcd tv is either 720p or 1080p so you would only need the 1 out.
“I'm the master of low expectations.” - GWB, 2003