If you have a fedora rescue cd, first installation disc from the cd set or the installtion dvd, you can boot into the rescue environment. At the boot prompt, you need to enter "linux rescue". The disc will boot to a shell prompt and to run fsck, you can do the following (assuming you used the default ext3)
Change /dev/hdX to the device name of the partition you want to run the filesystem check. If everything goes well, you can enter "reboot" to restart the computer.
If you do not have the Fedora discs I mentioned above, but have a live cd distro lying about somewhere, you can boot into it and run fsck from the CLI.
If you still experience problems regarding the root password, you can boot into single user mode and reset it. If you need more info on this, post back.