Mitch,
What you need to shop for is a composite video to VGA converter.
Assuming you live in North America, you are talking about NTSC composite video. That means all the video information comes down a single coaxial cable. All mixed together on this cable are several discrete signals needed to generate an image on a TV screen.
A computer monitor needs those different signals on individual wires, that is why you use a 15 pin monitor connector.
Add in that your computer monitor displays it's image with 3 important differences. a) It redraws the screen at a faster rate b) It does it from top to bottom, (the non-interlaced spec you see) TVs do it very other line line then goes back to the top and does the lines it missed first time (called interlaced) c) your computer monitor has roughly 2x the lines of resoultion of a Standard NTSC TV signal. 1024 lines computer Vs 525 lines TV.
A broadcast engineer could take me to task for some small errors in the above, but I simplified things for easier understanding.
That explains why just a cable will not work. You need an active converter. I would be suprised if you can get one for under USD $100.00. Broadcast ones cost thousands.
You might be disapointed with the results. "Blowing up" 525 video lines to 1024 lines might sound like a good idea, but you will just be seeing more of the imperfections and noise of your source. It is very much the same as enlarging an old snap shot.
If you do buy something, see if the store will let you try it out first, or let you return it for a refund.
Good luck,
Aud_Mot