"su - root" or "sudo" complains of incorrect password but normal root login works

If you are unable to sudo or su, there are a couple binaries that may need setuid as the root user. On Fedora, it may just be that the user you're trying to sudo/su with a user who is not in the wheel group (other distributions use the sudoers group instead of wheel).

If you're sure you user is in wheel, check permissions on the sudo and su binaries like this (you should logged in as root for doing so):