This is really frustrating, but when all was said and done it turned out to be a hardware problem. The power to the card was plugged in all right...but the other end of said power cord had a loose connection.
Thank you so much everybody for all your help.
On the plus side, I've learned more about rpm, the boot process and LILO than I probably would ever have learned otherwise. And for all the hassle it was installing the 5336 driver, at least I now do have the latest (and hopefully greatest) driver for my card.
Thanks again everybody.