How to you expect a portable electronic device to run without batteries? Built in fuel cell .... hand-crank dynamo.... solar panel array.....wind turbine....nuclear reactor? Or maybe it can be powered by Dark Matter or a Gamma Ray Burst? Well, once you have accepted that you'll need to settle for using batteries, go with either Nikon, Canon, or Olympus. Those 3 brands have the best optics. Forget large numbers of pixels and all that. What makes the difference is the quality and size of glass lenses. I'll take a 3megapixel quality lensed camera over a 10megapixel average quality anyday. This advice holds true for both still and video cameras. Your video recording time is dependent upon tape length or memory card size.
Your original request is worded as if you are asking the Fairy Godmother for such a fantasy device. Go visit the customer forums at on-line sellers like NewEgg.com or B&H Photo for owner comments.