I have the same symptoms on 16.04.1 LTS, since yesterday.
Seems like you have no choice but to long-press the power button. Start the computer again, and it shouldshow the Grub menu.
On the "Ubuntu" line, press your keyboard's
e key to edit the startup command. (In my experience every few times you do this, pressing
e has no effect or just jumps to the last line. In that case just reboot and try again.)
In the editor that appeared, at the end of the
linux line, add
nomodeset (to waste less time go down to the next line then press your keyboard's left arrow).
Press F10 to reboot.
In my experience (limited to 5 times so far) it most often does not work the first time, so repeat the procedure until it works, it may take 4 times. Sometimes it just worked like this, sometimes I tried booting the recovery kernel (same linux kernel version) which got stuck then rebooted again then did the nomodeset trick again then it worked, not sure if that helped or not.