SAAB 9-3 2003 Poltergeist?

Frequently there is no response at all when I turn the key. I wait awhile and after 10 to 60 min. it starts. If “waiting” were a legitimate fix-it, I’d be doing great. There is no pattern to the problem. I’ve ruled out temperature, time of day, miles driven, etc. Saab dealer did a “computer analysis” and charged me big bucks for a new starter. That made no difference.

It’s not a battery problem, apparently not an ignition problem. Is it a poltergeist?

If the dashboard warning lamps illuminate and there is not even a starter solenoid click sound when the key is turned the most likely suspects would be:
faulty neutral safety switch if the car has an automatic transmission.
faulty ignition switch.
security system glitch.
faulty clutch safety switch if the car has a manual transmission.

I’m assuming here the battery, the battery cable ends, and any cable distribution terminal are all good and clean.