It sounds like a sticky shutter latch. Will allow free winding of the advance lever but will not allow the shutter to fire.
Sometimes, after continually working, the latch will sit in place and allow firing of the shutter.
Sometimes, working continually will allow firing frequently of the shutter but leaving it for a short will returns the problem.
I'm not 100% certain but am pretty sure the same applies to the ME, as the above statements are definitely true for the ME Super.
Edit: When you say moving freely without resistance, do you mean that it will not wind on and that the lever seems disengaged from everything? Or would it wind on film if there was film in there, but not shutter?