Quote - (FusionOpz @ Sep 19 2008, 06:49)

^ I think I said the shifter button doesn't lock up like that when the car is off (aka not running), and I don't know of any cars with an automatic that'll start in neutral let alone shut off...
The other thing I forgot to mention, theres been a few times the car is in park (we generally don't use the parking brake) and it's started rolling once we release the brake...
And how can it not be in the tranny when I said it only does that when the car is running?
Yes the shifter button.
Hmm, my Scout II, Chevy truck, and Lincoln Town Car as well as the parent's accord, all autos, will all start and shut off in neutral. Most of my cars are manual though. Did you actually check the Cutlass?
If it starts rolling once you release the brake then I think it points to the transmission not actually engaging in park. I still think the problem might be in the shifter mechanism itself, but with the additional information it is looking like might be in the parking pin. I would start with the shifter mechanism as that will be easy to check and cheap to repair. Then move to the tranny as that will be harder to check and more expensive to repair.
In the meantime, if you can in fact start and shut off in neutral. Do so. You might be unable to remove the key though. I would defiantly use the parking brake as it seems Park is unreliable regardless. I might even go so far as the chock the wheels.