Why won't my 1999 Buick Park Ave start after I switch the trans from a 98 Buick?

Electronically incompatible transmission, ignition switch, wiring issues. Have you tried driving it yet to see if it will shift. To be a truly plug and play the transmission numbers must match.

Check you neutral safety switch

Yes I drove it and it shifts fine, goes through all the gears, For now I just put a starter button in it, but I still would like to figure out why it won't start with only using the key.

Then you will need the circuit diagram for the crank circuit and see if the voltage is where it needs to be during the crank position from the ignition switch to the park switch then to the starter solenoid. Maybe there is a pinched wire.