Windows 7 sticks at black "X programs need to close" screen, but neither keyboard nor mouse will work

Symptoms:  You try to shut down Windows 7, and it pulls up the black-background "programs need to close" screen.  You try to press either "Force restart" or "Cancel", but you can't - neither your keyboard nor your mouse will actually let you click either button.

Fix:  Try hitting Ctrl-Alt-Del to interrupt Windows and get to the logoff / shutdown screen.  The mouse and keyboard should be working then, in which case you can return to the previous screen, click "Cancel" and shut down the offending program properly.  Alternatively, you may be able to force a restart from the new screen.