I read ur post and the replies and I came to the following conclusion:

1) It could be the neutral safety switch. If it is old, replace it ( every 3-4 years is good). I replaced mine about 2 months ago.

2) I have the same problem, even after replacing the switch.

After I read ur post I got an idea.

When I put my car in park, I made sure I followed the gear shift all the way into park. It moves a little to left when u follow it to park.

My car started every time after I did that. My conclusion is that my 2 bushings on the transmission linkage is worn and has too much play. I am going to replace the 2 bushings and will let u know if that solves the problem.