Motor turns over but won't cranck

What is your question?

Which sensor/part acts as the points, as in an older car? Sometimes the motor won't start. It seems like the points need changed but there are no points. After a few minutes of not trying to cranck it, the motor will start up easily as normal. I have had at least 4 people to diagnose the engine with no answer to the problem. Where, besides the dealership, can I go locally to find someone who can properly diagnose the problem?