If I try to "su root" with an incorrect password, I get the expected 'authentication failure'.
If I try to with the correct password, I get 'setgid: Operation not permitted"
I have tried the usual 'boot via grub to reset the root password, but then I get 'bash: cannot set terminal process group (-1): Inappropriate ioctl for device' and need to power cycle for the keyboard even to be recognized.
I do not have sudo installed. I have not made any administrative changes to this machine in months, it was working as expected, and now suddenly is not.
This machine dual boots with Windows, and the root correct password does allow me to access the shared Windows hard drive. ("Authentication required to mount...blah blah..")
edit: ls -l $(which su) shows
-rwxr-xr-x 1 myname myname 40168 Nov 20 2014 /bin/su
Eventually I determined that I could not su to any user, not only to root.
Booted from a live CD
mount /dev/sda1 /mnt (sda1 in my case, maybe not yours)
chown -R root:root etc
chown -R root:root bin
..all the other directories that were accidentally mine, not root's
and most importantly, /bin/su needed to be -rwsr-xr-x
it was not just the ownership, but the 's', not 'x' for the owner that was tripping things up.
I suspect other issues will arise from incorrect ownership, but now that I can su to root I should be able to correct them.