I have a nikon cool pix camera that doesn't turn on
When there is nothing happening, it is hard to understand what is wrong.
Do the menus cone on or anything turn on?
If the camera comes on at all, then try setting all the menus to default.
If nothing comes on, no lights, nothing, then you are stuck.
If it will not turn on at all, I would recommend selling it at a site such as Ebay for repair parts, as is. At least you can get some money back, and buy another camera.
Also you may want to consider to call Nikon and trade-in or trade-up your camera for a re-furbished unit (a re-furbished unit will have everything just as it came from the factory. The support-repair department would be the place to get the number and information.