Chevrolet: My horrible lumina, solenoid switch, solenoid

Question
I got a 95 lumina in Jan. of this year, since then I have had three transmissions, new brakes, and recently put a new starter in. That was because for some reason when you try to start the car, it doesnt click over. Its making the sound but it wont turn over. And then i wait 15 or so minutes and mess with it a little and it will start up. I thought i was the starter but obviously its not. Could it be the solenoid switch or something? Ive gotton it looked at and they said it was one of three things. PLEASE HELP!

Answer
Sounds to me like dead spots on the starter but you say you changed the starter.

Does the battery have enough juice to turn over the starter?

The clicking you hear is the solenoid so it wouldn't be that. If the solenoid or the switch was bad you wouldn't hear anything.