I have the same problem. Its actually because the On/Off button got pushed in somehow and its stuck. At this time right now, im not sure how to make it unstuck, but sometimes it will stay on. But when you push on, since its being held down, its stuck that way and immediately turns off because its still being held down constantly. Maybe try using a thing needle to try and push it out?

First, is it charged?
Second, see if the screen says lens error...if it does then you might be holding the lens down when you try to turn it on.
If not, then maybe it is broken.
Hope this helps!