I'm running whichever version of Gnome is standard for Fedora Core 1. Earlier I was happily computing along when it crashed, for no particular reason. I was not running anything unusual and I do not believe it to be caused by any software I have installed in the past couple of days.

Where it gets scary is Gnome will not restart. I run startx an it takes me to a black screen with a cursor like you get when you run X by itself. I left it for several minutes on the off chance it was just being stupid or stubborn, but nothing happened.

It's not a huge problem, except that I prefer Gnome to KDE and I'd like to get it back to working properly. I don't know what LOG files to look in or where to go to find out what's wrong. Any help you guys could give me would be much appreciated.

try this:
as root at the command line type gdm and when the login screen comes up (if it comes up) go to session and choose gnome and then log in
let me know what happens

Nothing but a blue screen and a cursor.

well i dont know alot so i cant really tell you what to do but if all else fails you might as well download gnome and reinstall it :\