Here is what nikon says: "While Nikon takes great measures to assure high quality in its imaging products, it has come to our attention that an electronic component related to power control in some Nikon D5000 digital SLR cameras does not meet factory specifications and may, in certain circumstances, prevent the camera from turning on, thus preventing operation of the camera.
Indications of this issue include: The camera cannot be operated when the power switch is on, even with a fully-charged battery. The camera cannot be operated with the EH-5a AC Adapter connected through the EP-5 Power Connector and the power switch on. The solution: Nikon has isolated the issues related to this and is effectively resolving them. Preparations are under way at a special Nikon repair facility to streamline the processes associated to the solution and Nikon will be equipped to correct D5000 cameras at this facility, beginning July 23, 2009. Service related to this issue, including the cost of shipping affected D5000 cameras to Nikon, as well as their return to customers, will be free of charge. To further minimize customer inconvenience, Nikon will return serviced cameras to customers promptly, employing (whenever possible) transportation that limits transit time to two days. ...."
You can read the full Advisory from the nikon web site: