1999 Volkswagon Jetta 96,000 miles

:cry: My Jetta starter willl not crank sometimes. The battery is new. It will happen randomly. Sometimes after it has been stopped and started 3-5 times. Sometimes when it has not been started in days. Sometimes in the rain. Go back to start the car 10 minutes later or the next day and it starts right up. You will hear the musical sound when you turn the key and the dash idoit lights will come on but the starter will not engage and turn over. I tried starting it in neutral. That did not work. The solenoid that coordinates the brake pedal and allows you to shift out of park was replaced. The starter was checked to see if it was drawing to much but it was not. Thought it could it have something to do with the alarm arming itself and attempted to lock the car without setting the alarm but that did not work. If I bring it a mechanic he finds nothing wrong. Their statement was call me when you are stuck. Help.