Black screen with arrow only?

My Mac mini is only a few months old and still under AppleCare. I have had very few power outages or other forced shutdowns in that time. On a couple of occasions, however, my screen has suddenly gone black in the middle of using the computer.

I know it is not a monitor or mouse issue because I can still see my mouse pointer and move it around, but clicking does nothing (or it may do something, but I can't see what I'm clicking). Obviously, I cannot select shutdown or restart in this condition.

Assuming I should not ignore this issue, what troubleshooting steps should I take? Also, is there a way to shut down via keyboard that doesn't have a power key or if an app is running that tries to cancel shutdown?