I had this same problem, but i couldnt get the damn thing out of park unless i beat on the button. I took the console out to check things out. Under the console, up near where the cig lighter would, there is this black solenoid looking thing that connects to the shifter linkage from the button. I unhooked it for *****, and tested it. Problem was gone. I figured it was there for a reason, probably to prevent being able to put the car in neutral without the key in the ignition, so I tested that. With the key on, I can put the car in park and it will come out no problem, with the key off it locks like it's supposed to. That fixed the problem for me, so i left it like that...no problems since. I still don't know exactly what that black thing was for, but I dont care....it works great.
try pulling the connector off of it, and see if that fixes your problem. I bet it will. You might be able to get to it by removing that cubby hole next to the cig lighter, i think it is right under that hole, but I could be wrong. Try that before you pull the whole console.