After an update that included the kernel and a reboot, X no longer started for my Ubuntu 14.04 machine. An attempt to startx manually failed as well with this message:
Note: the underlying issue has been addressed by a more general question and answer and is linked in my answer below.
The line
modprobe: ERROR: could not insert 'nvidia_352': Required key not available
had the right clue. In a nutshell, the new kernel appears to not load unsigned third party modules (the Nvidia driver in my case). Disabling Secure Boot in the UEFI (BIOS) settings solved the problem. This answer helped me disable Secure Boot for my ASUS board a little faster.
This answer has good background, a possible alternative solution, and mentions the problem starts with kernel 4.4.0-20. In my case (Ubuntu 14.04), the kernel that caused problems is 3.16.0-77.
