Hmmmm, I've heard that RedHat 7.1 is really stable. Personally, I use Mandrake [8.1 now]. I had used RH6.x, but hated it.
I wish I could give you more info/help, but... from what you have said... is sounds like you mave have some sort of currupted X installation.
Can you still log in via tty/ssh/telnet? Are you using a graphical log-in screen?