New battery, new starter, sometimes car didn't start

The battery is about 6-month old and my mechanic replaced the starter last week as the car had a hard time to start. Since then it has no problem except once in a cold day (about 35 degrees) it took 10 minutes to get started. Every time I switched the key, no sound came from the starter or the engine, just like what happened with the old starter. But this only happened once. I didn’t have trouble in other occasions with the new battery and the new starter. What could be the problem?

Thanks in advance.

If it has an automatic transmission the problem might be with the park/neutral safety switch. The next time it won’t start, leave the ignition on, step on the brake pedal and shift into neutral and then try starting the engine. If the engine starts the problem is with the P/N safety switch.

If it has a manual transmission, there’s a clutch pedal interlock switch that prevents the starter from operating unless the clutch pedal is depressed. Unplugging the connector from the switch and inserting a jumper wire in the connector will take the switch out of the circuit. Now it can be determined if the clutch pedal interlock switch is causing the no-start condition.

Tester