The shift lever is stuck in park and the car won't start on 2004 Buick Rainier

When I put the key in the start position, all the dash lights go out. But a couple of times, when I pushed forward on the shift lever and turned the key to start, the car began turning over, just would not start.. Is there a problem with a switch on the shift and the starter?

Asked by for the 2004 Buick Rainier
This sounds like a problem with the neutral safety switch. Here it is: