Your LG flatscreen TV should have audio ports which are associated with the VGA PC input. Check your owners manual. You will likely need a 3.5mm stereo to RCA L/R adapter and cable. Aside from that, if your graphics card has an HDMI output, then the next easiest thing to do would be to run a 20'-25' HDMI cable.
Buying a new graphics card would be the last resort. It absolutely should not be necessary.