But just so we understand each other- when you say composite cable you mean rca jacks, right? I have a 20'Monster audio/video cable that has s-jack and rca jacks on both ends, so if you have cabling on both ends, you should be able to do it. Just make sure you go into your video properties to tweak the settings for incoming video to your monitor- could be settings for your video card- just check the manual or go online for your video card to find the right settings and where.
On the back of my video card, there's connections for both s-jack and rca. I don't know if you want to run audio into your computer or even if you're able to. If you're just running the video, maybe you can find a hybrid cable of some kind- s-jack on one end, rca on the other. Reason why I mention this is cuz the cables I got from Monster (they make really good cables) cost $40- a few bucks more, you can get a dedicated dvd player. I got the cabling I got cuz I wanted to capture the audio, which I ran into my Audigy SoundBlaster bay, which had the audio in ports that accepted the rca jacks- I guess there's adapters you can get from RadioShack that can convert a mini-jack to rca; can't say I know for sure, as I never looked, but there's cabling/adapters for everything it seems. Good luck. Hope this helps.