1998 Honda Prelude Intermittent starting problem

My car will always start in the morning and when I leave work but sometime when I stop somewhere the car won't restart. My headlights is bright and the radio works. When I try to turn the ignition, I don't hear any noises. My battery is less then 1 year old and rated with more power then what my car needs. The alternator(less then a year old) was check at Kragen and was told it was good. The starter is less then a year old. I also had the check light 420 so I took it to a shop and was told it was the Cat. Converter that might be causing the engine to not start. I replace that but the problem still exist. The check light did go away. The mechanic nows says its might be a defective starter but I'm a little weary since I already spend 1100 on the cat converter and cleaning out the engine oil ( They said I needed this so they could diagnose the problem)

Things I noticed:
Sometime when I get home, I turn the car off and immediately try to restart it and sometime it won't start. It will start the next day.

The car will start immediately when jumping the car and I could go somewhere and start it again without any problem.

I tried those portable car charger but it won't start the car. A jump by another car will start immediately.

Leaving the car for one to two hours sometime still won't start but recently the weather has been really hot if that has to do with anything. There was one time when I left the mall at 7:00 pm and the weather was cold and it didn't start. Only after a jump and started fine the next day as usual.

I am at the point where I'm afraid to go anywhere. Thank you for your time, if you could figure this out I be really grateful.