So happy I found this place! I have a new Kindle 2, about a month old, similar as to the OP. Just today was reading on it, turned it off, went to bed, decided to read a little more, noticed the green power LED was on. Hmmm... turning it on or off did nothing, only displayed the same screen all the time. Found this place...rest is history.
Followed your instructions for the K2, held the switch for 20 seconds, but got excited when the LED went off and touched it again!!! Don't do that!
Went back, held the switch for 20 seconds, LED went out, laid it down and within a minute it was rebooting. Took it longer than normal, waited until it was complete, tested both on and off and works fine. Plugged into the puter, fully charged so wasn't battery related.
Seems to be functioning fine now, but glad I read here before I tried taking it apart! Great forums!!!!