Unreliable starting. Turn the key to the start position and nothing. Dash light are illuminated etc. . Exact response as if trying to start the car while in gear.

This started about a month ago- had 3-4 occurences in a two week period. Let it sit for a while ( no specific length of time) as short as 3 hours, as long as overnight, and it starts fine on multiple successive tries.
There seems to be no correlation between the temperature of the engine and the symptoms.

Replaced the neutral safety switch two weeks ago, and no problem until this afternoon. This time I had driven the car 140 miles with 3 stops and starts. Turned off the car at 2p back at home ; went out to start at 5p and experienced the same symptoms as previously. Tried again about 7p and it started fine the first time and again on 3 successive times.

Any feedback would be appreciated. Possibly the ignition switch or starter?