Not really a client, but stupid nevertheless.
School Librarian: You can't use that computer, it's broken.
Me: It is? How?
SL: It doesn't work, leave it alone. (leaves).
I look around the back and, lo and behold, the monitor is unplugged. This has happened several times, with the exact same dialogue every time. What's worse, the procedure for computers that are actually broken is putting a "Does not work" sign on it and dumping it in the corner in a Tetris-like stack.