Chevrolet: chevey cavalier 2000, starter solenoid, starter motor

Question
afterturning off car and restarting  it won't turn over. have to let it be for about 1/2 hour then it will start its at the mechanics car dealer and they can't find it ran computer diagnostic they drove it for a couple of hours and it was ok as we got into it and started it it starts got to end of parking lot and it stops they pushed it back on lot and just for fun i turned it on and it started ?? its costing lost of hrs labor and no results
can you help me with a answer

Answer
Linda;
HI  well the first thing I would do is to replace the starter motor and solenoid, as the fields in the starter/solenoid get hot and will not allow the solenoid to pop into gear to function. and have the battery checked for the voltage output , from the alternator  and from the battery.  also  have then check to see if the ex.pipe is too close to the starter motor. or if it is, tell them to rap it with some heat proofinf to cut down on the heat to the starter,ok