Nikon has published a service advisory related to a power issue with some samples of DSLR camera D5000. Basically, there is an electronic component which prevents camera to switch on in some conditions (fully charged battery or adapter with power connector). No safety risk involved.
Nikon will publish on its website serials of cameras that can be affected by the problem and is preparing a free repairing program.
The original advisory from Nikon is reachable at this link.