The way my Fuji GW690's shutter died was by firing it in T mode with a several minute exposure. This is because there was dirty grease on the shutter blades which eventually caused them to stick together.
After that, you could get it to fire and the shutter blades moved, but not enough to open/close. Agreed with others that said it's a sign it needs servicing.
Yours might be that, or some other part that's sticking. I'd gently try all permutations I could of the controls without forcing anything too hard.
Oh, and some cameras work if you activate them by cable release instead of the normal trigger.