Having the exact issues now...have to use neutral sometimes to start. Heat is also a catalyst, typically the issue arises after a long drive then a short park. If the neutral thing doesn't work time does, once cooled ~30 miins it will start up.
Time to call for a new switch....
Well after reading Stealthbob's post above, I decided to test that theory.
This problem only seems to happen to my wife every few weeks and I thought maybe she doesn't drive it long enough to get that hot to affect the switch.
So, in the car we both get and drive for 45 minutes down the highway to a restaurant.
Sure enough, I turn off the car and try to start it again, nothing.
Put it in neutral, starts right up.
Try again in Park, nothing.
Try again in neutral, starts right up.
I did this 4 times and each time in Park it would not turn over, but it worked every time in neutral.
We went into the restaurant for about 45 minutes, came out and it started right up in Park.
I guess it cooled down enough.
I drove 5 minutes to a butchery and tried immediately to start it again and it would not turn over in Park.
I also noticed something really neat...
The shift position indicator on the dash has a square box indicator that lights up around whatever gear you are in.
When I am in Park, and there is no box indicator around it, then I know that it is not going to turn over because the starter is not going to be getting any power.
You shift to neutral, the box appears, and you know you will be able to start.
I put it back in Park, no box... I wait, and wait, and wait, suddenly the box appears around the "P" and I know that I can now start the car.
So, it appears that the problem is not the starter, or the battery, or corrosion, or the cables as we were all guessing.
It is the Transaxle Range Switch located in the engine compartment under the breather that is affected with the heat of the engine.
Thanks Stealthbob, you were bang on.
Now I just have to figure out how to change this thing.