How do I playback video on Canon Powershot SD600?

SOURCE: Canon Powershot SD600

In shooting mode press DISP. The display mode changes with each press.

Standard>Detailed>Off

I think you have it currently set to off.

SOURCE: battery fully charged. but canon powershot sd600

Your problem may be due to worn out batteries or corrosion on the battery contacts inside the camera which can prevent the full power of the batteries from flowing into the camera. Try this free fix before you do anything else: remove the batteries and wipe the camera contacts firmly with a dry cloth (heavy corrosion may require cleaning with a wire brush, steel wool, or sandpaper). Remove any residue that may have fallen into the battery compartment during cleaning, then wipe both ends of the batteries and place them back in the camera. This cleaning clears the problem about 90% of the time. If it doesn't work for you, chances are that your batteries need to be replaced because they're just too worn to properly power the camera. And then, of course, there's the possibility that your camera may have a problem that requires professional repair.