Look, to be honest, if the livecd works, and the mouse works in there, then there is a problem in installation; the version of Fedora obviously works with your setup, else it'd error on the livecd. Use the livecd to back up your files and do a clean install.
To back your files up, you can either connect it to an external HDD, copy to a series of dvds/cds/floppy disks, copy over a network, save to a partition on your HDD that the Fedora installation isn't going to overwrite, print a byte-by-byte output of the disk through your printer and then use OCR to write it back or any; once you're in the LiveCD environment, you'll be able to use your mouse again.
What I'm suggesting, then, is to just re-install fedora. If you've just installed it, you shouldn't be losing too much, though you can use
to see what is installed; save that output too and you'll know what to install afterwards.