I can't find the NSS (neutral safety switch) on my wife's 95 Dodge Avenger 2.5L V6 car. I'm pretty sure that's what's causing the problem. The symptoms are... won't start in park but will in neutral, doesn't want to go into park, car is stuck in 2nd gear and won't go into drive even in the "D" position and if you do attempt to put car into park reverse is still engaged as well but you can turn back and take the key out.

 

I think your problem lies on the shifter itself. I had that problem a few years back and it ended up being the rod that catch on the steps..lol, I know that sounds weird, you just have to take the center console off and the sides and look and you will see what it is that I'm talking about. It's been so long ago though, I'm not exactly sure what I did. Nonetheless, that's where your problem is.
Just to make sure, my symptoms were...when I put it into "D" it was in "N" instead, park was actually reverse and so on. If that's what you're symptoms are then start there. When you have all that stuff off and when you put it into different gears, you'll see what I'm talking about.
Hope that helped some...sorry I couldn't remember what I did to fix it though.

 

Well, here's a breakdown of what the car acts like when it's in certain gears...
P = combination of P and R
R = normal
N = normal
D = 2nd gear
2 = normal
1 = normal
To start it, have to move from P to N, then start the car. To turn it off, have to shove it in P, pull e-brake, then turn it off.

 

My first place would have to be the actual shifter. Most of our problems start with the fluid, but in this case I would start with the shifter --> then the clutch pack --> then the tranny. This happens when the car is still cold...fluid...but since this happens at any temp and time of day, start with the shifter.