If holding the switch for an extended time does not work, take a deep breath and resist the urge to fling your Kindle against the wall. Then find a safe place where the unit will not be touched and leave it for 3-4 days. You may need to wait for as much as a week. Once the battery has lost some or all of its charge, try plugging it in to recharge again. No promises, but when my screen froze this worked. The idea came from my daughter, who has similar issues with her iPod from time to time.
Good luck!