This sounds like an urban myth but it actually worked on my 1020 which was fully charged, and had been unresponsive for a week, despite trying all of the resets that usually work.
If you're using the battery pack extender, remove it. Then wrap your phone in a plastic bag and place it in a deep freeze for an hour. Reconnect it to the charger and just leave it alone, mine resets after about an hour when it gets back to room temperature.
This fix was passed on to me by an auto electrician who says its an old trick used to reset some car stereos after the car battery has been replaced incorrectly. Worked for me (he claims 60% success rate; but sorry, no promises).
Nokia/Microsoft, it's frustrating that we have to mess around like this.