Gear issues?

Have a 2001 Toyota Corolla, automatic transmission. We replaced the transmission with a transmission from a 2000 and we've had problems ever since. The car won't park, the gear shifter goes into park but the car doesn't know it's in park, drove like that for a while and today, no matter what gear I put it in all it does is reverse.
Replace this part and you will be good to go.Toyota has an improved version of the part...ask your dealer.

That's not the issue, the gear shifter works just fine, and goes through all the gears. It's just not registering with the car. My dad thinks it's the neutral safety switch, but I think it's something else but we know it's not that part, thanks