You are describing a sticking shutter.
The movie mode should be unaffected and will confirm the shutter sticks.
Put the camera into full optical zoom, turn off the flash, now look into the lens and press the picture button. When you take a picture shutter leafs will close across the lens iris completely covering it. Over exposed pictures in daylight or lines across pictures indoors is caused by the shutter leafs not closing completely over the iris. Cleaning is possible if you take it to someone who has done this before otherwise fuji will replace the lens - at cost!
Dave- camera repairs, February 2011