It probably is your starter solenoid, becasue I had the same problem, I had a starter like that for about 2-3 months. I would have to get ready for work about 15 mins early so I could go outside and play with the car to get it to start.

Try taking a hammer or a long piece of metal and hit it with a hammer on the starter. Then try and start it. If the solenoid is stuck, a hit with a hammer will fix it. Then you just need a new starter. But that has worked for me on many cars I have worked on.