May or may not have anything to do with your problem however, I had an old Roper/Craftsman 3.7 come in that was doing the same thing. Just as you said starter worked great off the saw and saw turned easily without starter.
Turned out that the back of the starter pulley had a hairline crack in the back, which would not force the starter cord to wind up on top of itself between the sides of the pulley. Cord would wind up parallel to itself, forcing the pulley sides to flair out and bind against the starter housing, locking the saw up tight! Not immediately evident that the pulley was damaged because the crack was right at the hub and on the side facing away from the saw. And this was a pot metal pulley not plastic, when it would lock up it was metal against metal and there was no way to pull the saw over it would just stop dead!
Installed new pulley, big PITA on this saw, everything worked fine with new pulley installed.