What would cause intermittent starting problem?

What is your question?

It cranks fine in the morning and then a long crank after I kill it for about 10-15 minutes but starts. Normally it won't start after I kill it for about 45 minutes. It eventually starts after waiting a random amount of time like 30 minutes to an hour. Would a leaking catalytic convertor or bad coil pack cause? Its not the starter relay, battery or alternator. They are all new. I'm at a loss.