Does your fuel pump buzz when you turn on the ignition switch, just before you crank. If the fuel pump buzz is heard, the starter lock out switch is likely fine, because if you are in any other gear but park and neutral, both the fuel pump relay as well as the starter coil does not get any power.

So that leaves the starter coil as the culprit. You can check resistance and see if there is any open circuit.

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Saumil S. Patel