first off how far away from your tv is your pc? i would recommend trying DVI to HDMI as long as you buy a high quality HDMI lead i.e spend over £100 on one and you should be ok ecause it is a digital signal you wont lose quality.
your problem could lie within your graphics card i have experienced problems with nvidia graphics cards when trying to connect to a tv in that although i could get the cloned image via an s-video connection when i tried to watch a video i got the image on my pc but not on my tv i think its just a problem with nvidia cards in general try an ati card i find them excellent for connecting to tv or try connecting trough s-video if your tv has one but i am sure it has being an LG