root is the super user of the system, there for you need to be
in what is called single user state and if you look at the web site
Roy sent you about 4 bullet items down it mentions getting to the single
user state.
In order to change the root password you will need to enter the command:

passwd root

Just like that, the system will ask you for the new password, enter what
you want the new password to be. That is the same as the admin
password.

To get a new distribution you will need to have a CD burner which you
may have on this used Laptop in order to burn a new image which you will
be able to download from the Fedora site. If you have a CD burner you
then need to use an image burner to create a new "live CD" which you can
boot from and load onto the PC.

This can be a real fun time ahead leaning this new system.

Good Luck and come back with more questions when you have them.