You probably know this, but the cocking lever needs to be moved twice. If you can't press the shutter release button down, then there's your problem. If you can push it down but nothing happens, the shutter may indeed be broken.

Fuji GWs seem to have some problems with drying lubricant in the rangefinder mechanism. When mine arrived, the rangefinder didn't work either. It suddenly started working after 30min of focusing around and has been functioning excellent ever since. Maybe this works for you too, I don't know.

Good luck, they're awesome cameras.