Car started but confused on 1998 Ford Contour

When I turn the key in the ignition the dash lights come on, the fuel pump works but the engine do not turn over nor does the starter. So I turn the key in the on position and slowly shift through the gears then the car started. How is this possible

Asked by for the 1998 Ford Contour
It sounds like the neutral safety switch (also called the inhibitor switch) is bad. The neutral safety switch prevents an automatic transmission car starting "in gear". By moving the shift lever position you may just make sufficient contact across the electrical switch to get the car to start. The neutral safety switch passes power to the starter from the ignition switch only when the transmission is in Park or Neutral.
where this switch located and how to replace it
I have same problem and I changed starter,neutral safety switch,starter relay and battery. What now???????Maybe ignition switch???????
2 answers 2 comments
You car is automatic transmition and there is a switch to control the starting while in gear so you need to change that