Fred Hansbrough, make sure that your lens is properly seated. Your camera will not turn on with a dislodged lens. the other thing to look for is in your battery "door" Take a close look at it, you should see a micro switch that will prevent the camera from turning on (or it will turn off) when the battery is removed. Sometimes that switch gets stuck, or the little nib may even break off. You can try to use a safety pin to depress the switch and see if the camera will turn on. If you find that it is not caused by the battery cover switch, you may have to disassemble your camera and check fuse F601 DC-DC Converter on the main power PCB and make sure that it has continuity. If you need it, you can download the service manual by scrolling to "Documents" on this this page. Of course make sure that your battery contacts are nice and clean and you could try to connect the USB cord to your computer, putting in the battery, and pressing play. Hope that this will work for you. Let us know and good luck.
Somebody woke up this old question ;-) so here is an image of where the fuse is located