Ive got an 87 GTU that has been giving me starting problems, But not fuel/flooding related.

The starter was replaced before I bought the car. So its relativly "new".. but

Its seems to get power to the starter. You can here the solenoid "whine" but it wont send the gear to the flywheel. Ive got a solid 12v on the battery, no dummy lights.
When the starter will start the car, you can shut it off and start it right back up.

Any help would be great..