I stowed away the old laptop that I had Fedora 10 on. See if running in single mode (add an `s' to the end of the boot options) gets you in a shell as root without a password. If not, run the installer disk and select "rescue" or use a live distro.
The first problem is mounting the Logical Volumes. You want to access the root partition (/) to edit the /etc/shadow.
IIRC, you need to run mkblkdevs so that the device nodes of the logical volumes are created when booting up in a live distro or rescue mode. Please check the manpage on this.
lvscan can tell you which logical volumes are present. The default config AFAIK has a /boot partition and a single LVM2 physical partition.
Once the root partition is mounted, you can edit the /etc/shadow file. Deleting the characters between the first two colons :....: will zero out the root password. I did do this once after I somehow skipped the root password prompt when doing a fresh upgrade, and found that the system was configured so that you couldn't log in with null passwords. So instead, I copied the characters between the colons from my regular user password hash (/etc/shadow) and pasted these same characters in the root users entry. Then I was able to reboot and log in as root using my regular users password. Next I run the "passwd" command to set the root password right away.