I had this problem, and it persisted through battery change, Kubrick, etc. Finally, I bought a replacement motherboard, and all is well. No problem with registering the Kindle, which is a worry when dealing with used motherboards which could be from blacklisted Kindles. No problem here:
http://www.powerbookmedic.com/
Fairly fast service (well, 2 weeks at surface rate), decent price, etc. I ordered another motherboard for a second dead Kindle 3.