Thanks for all your suggestions.

Now having tracked down the problem to the keyboard, I pulled it off and blew it out. The key is functioning correctly (testing with a multimeter), but There must be something else wrong on the keyboard circuit. I did "exercise" it for a while. But when it is plugged in I get a definite beep response from pressing the control key, I am not sure what it thinks has been pressed and whether that beep is an error.

I looked over the circuit board from the back and it is fairly clean except for some dark marks around the ribbon connector.

I suppose I am just on the hunt for a replacement keyboard.