How to test which button is stuck
You could probably hack something together with autohotkey, it has functions to detect keystates.
Try PassMark Keyboard test This program allows you to press a key combination and a graphical display of the keyboard appears on screen. It tells you which keys the computer thinks you are pressing and then you can determine which keys are stuck.
Further to the suggestion of using something written in AutoHotkey, it seems that someone has already done it: osdHotkey. Very useful indeed.