Indeed that pin that signals to the body if a back is attached can become worn, bent etc.

There is another lock that wont allow the camera to fire with the darkslide left in and it also will not allow you to remove the back if the darkslide is NOT inserted.

It's hard to say without handeling the camera but according to your provided info it sounds as if it's ready for a CLA.

It's well worth getting one of these setup correctly.
Only thing about a straight "c" body is that it requires a tech (or the knowhow & tools) to switch out the focussing screen