1990 Cadillac Fleetwood car will not start

The car will not start. I pulled the starter and had it checked out (with the solenoid attached to the side). Both the starter and solenoid are in good shape and working. I also pulled the battery, yet again in good shape. When I put the starter back into the car, it just clicks like the solenoid is burned out. The car does not have the solenoid up top, just attached to the starter itself. I turned the motor to make sure it is not binding up and the crank and pulleys turn freely. I checked the wiring with a voltmeter and all is good. Am I missing something here? Question (Follow Up): The problem was the neutral safety switch. I replaced and now the car works fine.