2001 mustang gt,all access. work fully charged

Check your neutral safety switch with test light.

I would suspect the starter solenoid has failed.

A starter solenoid (or starter relay) is the part of an automobile which relays a large electric current to the starter motor, which in turn sets the engine in motion. In many vehicles the solenoid also engages the starter pinion with the ring gear of the engine.

The starter solenoid receives a large electric current from the car battery and a small electric current from the ignition switch. When the ignition switch is turned on, a small electric current is sent to the starter solenoid. This causes the starter solenoid to close a pair of heavy contacts, thus relaying a large electric current to the starter motor, which in turn sets the engine in motion. The starter motor is an electric motor that initiates piston motion in a car's internal combustion engine before it can power itself.