98 S70 - Ignition Problem - Car won't start, then will.

We have a 98 S70 Turbo with 143M miles on it. For the past year we have had a problem that sounds vaguely familiar to others that I have seen posted, but I am hoping to determine my next plan of attack.

For no apparent reason, sometimes when I insert the ignition key and turn it, nothing happens. When I say "nothing", the standard dash idiot lights turn on, but there are no other signs that the car realizes it is now supposed to send electrical power to the starter. If I am patient and wait for "awhile", I can try again, and the car will start. Sometimes the "awhile" is 20 or 30 seconds. Sometimes 15 or 20 minutes. Sometimes an hour. No rhyme or reason. The problem does not seem to be temperature related, because it can happen the 1st thing in the morning after 10 hours of garage time.

The Dealer and 2 other mechanics have had several shots at trying to figure it out, but, of course, when the car is in their possession it doesn't happen. The shift interlock (?) switch, starter/starter solenoid and battery have been replaced. No impact.

So, what's next? I was thinking about replacing the Ignition Switch, just to see what happens, but there sounds like there are other things I should consider (besides buying a Honda next time). Could it be the Ignition Lock & Cylinder (ka-ching, ka-ching)? Could it be the ECM (KA-CHING, KA-CHING)?

I just would like a plan of attack so I can go back to worrying about other stuff, like what to do about the crappy AM Radio reception, the faulty remote mirror control, and the power antenna that isn't.

Thanks for any input or ideas.