make sure your shifter linkage is not funked. My guess is that its out of alignment and may be the cause of the constant up and down shifts given that you don't have reverse. If you had reverse, then I would start looking at the throttle valve linkage adjustment at the throttle body, dialing it back in.
Do a simple test. Park on level ground and put the car in park. Get someone to push on the car and try to roll it. If it goes no where, you've established a base mark: Parking engaugement works. It may take some extra effort as this may be the lock up for reverse, so perhaps two people pushing the car backwards is necessary. Regardless, be ready to punch the brakes if it starts to roll so you don't hit anything while "ghost riding the whip."
If it rolls than your linkage needs adjusted. If it doesn't, then move on.
From park, depress the shifter button and slowly draw the shifter back. You may feel the car go into reverse but not be against the gates of the shifter. This is not a cure, it again means that your linkage is out of adjustment.
I don't own one of these cars, however I've screwed with my own AOD problems before. I'm not sure what type of indicator is in these birds, so take this with a grain of salt. If they are an indicator that has a bar that swings under a piece of clear plastic (not just dummy lights on the council next to the shifter), and for any reason it does not show that you are in park when the shifter is all the way foreward, or that you are in first when the shifter is all the way back, or sit square under the R,N,D,2,1 when engauged, consider your linkage out of adjustment.
Test and address.