Hey. Unfortunately, graphics card does not render videos, it just displays what is available. Since your graphics card is GTS 240, it's already fast enough for watching videos and buying a new graphics card will not affect their quality at all.
I'm sure if you go to www.youtube.com and search for a "1080p" video, and play it at 1080p setting in fullscreen it will look great.
The only solution to your problem would probably be finding a better quality stream.