On the F3 is the battery is weak the LCD won't turn on before the battery voltage is low enough to cause malfunction. I do think it's the foam. As the camera started its cycle by releasing the the mirror. The mirror has to complete its travel before it will trip the shutter. It's the mirror mechanism that will trip the shutter.
Originally Posted by NB23
If the shutter opened and closed but the mirror stayed up then it's because the foam is sticky and holding it up. If the mirror went up but the shutter didn't open then the mirror didn't travel all the way up. Try pushing it up might help to complete the cycle. Sometimes someone replace the foam and put in too thick foam strip and it would cause this problem.