MacOS – How to break out of a stuck lock screen

On a MacBook Pro (the office's, I'm a noob), I started the upgrade process from Mavericks to El-Capitan from the app store.

After a while, the screen locked as, I assume, is usual. But now I cannot log back in. I typed my user's password in and hit enter, nothing. I tried hitting the the little arrow button to the right of the password and nothing. It's not frozen as the mouse still works, no beachball, I can clear the password. I clicked on the Cancel and Switch User buttons which appear to activate, but then did nothing.

That was the case for quite a while, then I tried clicking the Switch User button again, and the desktop rotated like a cube and now gives me a light grey screen.