No "hanging of the starter" by definition.
I even pushed the car to get a rolling start (did not work)
It does seem to be a contact or immobilizer issue.
I think Marcel was describing a sticking starter solenoid, the one that sits on top of starter motor. The armature can corrode and stick in casing, hence a tap with (soft) hammer freeing it. This usually manifests as loud click and no starting action though.
I would also go with immobiliser issue.