The idea that the problem started after the transmission replacement is odd. The only thing I can think of is if something was disconnected.
If you have a spare key, see if that makes a difference. If there is no change, I have a feeling the immobilizer module will need to be reprogrammed.
I attached the directions below for reprogramming. It does require a factory scan tool or one that can communicate with the modules.
Take a look through the directions and let me know if you have questions.
See pics below.
Images (Click to make bigger)
Sunday, November 27th, 2022 AT 10:01 PM