Question has this car ever had a aftermarket security system added ?
I ask because a girl friend of mine had a similar problem with a little Nissan pick up truck. She/we never knew the remnants of such a security system was still wired in under the dash. It wasn't discovered until after I installed a new starter.
Funny thing is.. For a couple years She had got out and rocked the truck. All she really needed to do was open and close the drivers door again. Cycling the dome lamp circuit was resetting the security unit.
I really don't think your turning the engine by hand is having any effect on the electrical operation of the starter.