After an in-depth internet search, I had failed to find a device which would take those red, white, and yellow composite cables and output to either a VGA or DVI monitor connection. I had begun to think that it wouldn't work right and so no one had bothered.
Nonsense! It wasn't until I had physically seen one in a college campus common room that I discovered just such a device. It is called the Video Game Jockey, made by Startech, and it is fabulous. I have tried it and it works wonderfully. Your monitor will need to have a VGA input, and although it's an old technology many monitors still have it.
There are, of course, Ebay retailers who sell the device for much cheaper than Startech's homepage. You can expect to pay around $50 including shipping.

