I believe I have your answer.
Something about a recent Fedora update was to much for ATI's rubbish linux driver to understand, and so now it just keels over a few seconds after X is loaded, crashing the system in the process.
The solution is:
-At the grub bootloader menu screen press 'a'.
-At the end of the boot command you are presented with, add a space, then the word 'single' (no quotes).
-Fedora will load you into single-user, command line mode. Go to /usr/share/ati and do an 'ls'.
-There should be a load of bash scripts in there. Run the one with 'uninstall' in its name ('sh' followed by the filename)
-When that's run, run 'rm /etc/X11/xorg.conf'. Don't worry, F10 doesn't actually need that file. It's special like that.
-Reboot. Fedora should boot properly in full graphical mode, albeit with the default graphics driver.
-Wait for ATI to learn how to write drivers properly. This may take some time.