Were you ever able to come up with a solution. I have a 510 work car that I am letting a neighbor use. I used it as a work car for years but all in all it only has about 130 K on it.
I am having the same problem. I have all power (not sure of radio or not). It will not turn over or anything. I thought it may have been a relay switch since when you are moving the shifter (this car is automatic----you can hear the relay clicking)
Anyway, the car had done this to me a few times when I was driving it but I always moved the gear shift around a few times and it would start. I alwys thought the car was just not recognizing it was in park or neutral but as of right now nothing has got it to start.
Hoping by chance you or someone else may read this and have an answer.