However, I can boot my system and log in as any user, but I can't do anything with the system since I don't have root priviledges.
I kind of doubt it's all that corrupt if users can login ok.
Login to level 1 ( one ) by appending init 1 to the end of the boot loader.
This will allow you to changed the root passwd without knowing it first.
title Fedora Core
kernel /boot/vmlinuz-2.6.12-1.1447_FC4 ro root=LABEL=/ rhgb quiet init 1