Yep, I've had this happen after CLA'ing an M2.
The issue is that at the top of the film takeup spool, is a plate with a cutout. This cutout must be positioned to allow the shutter button to be pushed, when the shutter is cocked. Now, this plate (and its gearing) has a bit of play in it. This play is the related to the permissible back-travel of the shutter tensioning gear train.
I was "one tooth off" when I reassembled the M, and it behaved exactly as you described. No film, worked fine. With film, the film put enough backtension on the plate so that the shutter button could not travel downwards.
Easy fix once you know what is going on.
Vick