While The Camera Should Fire the Flash When In Auto Mode, There Is a "No Flash" setting available on the top of the camera. Be Sure that you are in the auto mode, as signaled by the Green Camera Icon Also, the Flash will pop up when you take the picture, so be sure nothing is blocking it, weather it be Debris or the Brim of your hat.
One of the problems that you may have could be related to battery issues: Try replacing the AA batteries within the camera. You may also have encountered water damage, which can possibly fixed with a Thirsty bag