First, if your car should not "crank" while the shifter is in any selection other than"P" or "N", check the neutral safety switch and wiring, or something is energising the "PPL" wire after the "N:" switch, or something is wrong with the "PPL" wire from the "N" switch to the starter.
I gather from your description of the fault, switched 12V power is engaging your starter solenoid, I say it is "switched" because you state it stops when you shut the car off.
1) check for installed aftermarket remote start hardware faults
2) check for installed aftermarket alarm system hardware faults
3) Check for general buggery.
4) I only have wiring diagram for 98-02, other years could be different.
