I figured this out.
It turns out, the F6 key was very slightly pushed over, and stuck under the plastic lip (from the factory), causing it to be permanently pushed "on". It seems that Apple kills a keyboard if it sees the same key press for too long.
Gently pushing the key sideways unstuck it and immediately the keyboard sprang into life. Even some of the fancy keys (volume/play/mute) work. Awesome!
MS - You made a great product that turned into a disaster. This could have been fixed with better manufacturing tolerances, or a better factory test/QA process!