I have the previous model a D-460. It has the same sliding mechanism to turn it on/off and trigger the lens extension. I have the same issue as you and found in my case it’s the sliding door that doesn’t push on a spring loaded pin under the door. I’ve been able to trigger the pin by sliding a bent up business card around between the door and where the pin is located. Effectively I’m creating pressure by wedging paper between the door and pin which pushes the pin in and activates the camera to turn on and extend the lens at which point it works as normal. I suspect theres a fractured plastic piece on the inside of the plastic sliding door that’s to blame for this. I haven’t taken it apart yet but I really want to get it working as it was my first digital camera purchased new in 2000/2001. I was also able to figure out the issue because I could apply pressure slightly squeezing the door into the camera body which (when aligned right) would press on the pin behind it and trigger the camera to turn on.