Then, second phase would be to create a new admin user account, log into it, and launch Font Book. If it launches, then your original user account is the culprit.
If you get the same behavior, then it's probably time to consider doing an Archive & Install, saving user and network settings, installation. Either that or seeing if the problem exists on your bootable backup copy. If not, then erase the original and clone the backup back. No backup, then A&I.