Sometimes my 1999 Honda Accord EX V6 will not start. on 1999 Honda Accord

We hear it trying to turn over but it won't start. After about 30 minutes it starts. It only happens every few weeks. When it happens all of the lights in the car will come on, but the car won't start. We have replaced the battery, the alternator and we have had the exhaust system cleaned out. Any ideas would be appreciated.

Asked by for the 1999 Honda Accord
When it WON'T start , and you turn the key to 'on' position , does the check engine light come on , or is it dark , and then when it finally does start , the check engine light is normal?