The f5 key on my Toshiba laptop keyboard appears to be pressing itself. I have a keyboard testing program and according to it the f5 key randomly becomes stuck, then randomly becomes unstuck. I can remove, press and move the key but this doesn't make any difference. Any ideas? And would getting a new key make any difference, as it appears to be the actual sensor which is stuck as opposed to the removable key?

Did you spill something on the keyboard? It is likely, as you said, that there is a short in the board itself and won't be fixed by replacing the key.