Yesterday my girlfriend’s '99 Saturn SL2 failed to start shortly after she turned it off. I checked the battery charge and then replaced the starter motor. The car started fine but the starter continued to spin. This continued after the ignition was turned off and the key removed. I disconected the battery terminal and replaced the starter relay. The problem persists as the starter will spin whenever the terminal is connected. Any ideas?
See if the starter will turn when the starter relay is removed. If it does, use a DVM to check continuity between the battery cable and the solenoid coil lead. If there is no continuity, disconnect the solenoid coil lead and reconnect the battery cable. If the starter turns, the problem is likely in the starter. You might remove the starter and see if it still spins when you connect it up to the battery with jumper cables. You might see that the pinion does not snap back to its resting position. I guess you could also take the starter back to the parts store and have them put it on their tester.
Good luck. Let us know what you find.