If it was a shutter issue it would mean that in M the exposure would be off. In S and P mode the lens must be put in to the max, f22. That way the aperture has full range of motion. The F4 then stops its lever at what it thinks is the appropriate spot along the liner travel of the aperture lever.
If the lever as I described above doesn't or can't got the full range then the lens would continue to stop down, and that I think is what is causing the under exposure. You need to check that lever inside the f4 as its shooting, try it in S and P and get back to us.