[Avisitor]

Ouch, tough to hear that you had to change the engine, .... AND the transmission??
This and the wiring harness??
OMG, you have gotten yourself into one big headache. Sorry.
First thing to do is to download a service manual
Google it or check the Gen 1 forum for a link??
And then look at the schematics for the starting circuit.

The park neutral safety switch is not aligned correct
if the indicator shows it is not in the proper gear
Also if the gear indicator doesn't show the correct gear
then how would the ECM know if it is in the right gear?
I don't know?? I would check to make sure the engine will turn.
Either crank by hand or by using a wire from the starter solenoid to B+.

The key not coming out is just another thing that shows the gear is not in park????
I wish you much luck in getting this engine to run again.

 

[Avisitor]

Why doesn't the gear selection indicator not showing the right gear?
Did you check to see if the engine will rotate? (either by hand crank or B+ to starter solenoid)?
Just thinking about how the wiring must be correct for the key to turn to crank and engine to start??
Check the fuses and see if there is power going to the starter cut relay (when key is in crank)??

 

[Avisitor]

Do you have the service manual? Might help with the wiring??

https://www.workshopservicemanual.com/m007275-honda-crv-rd1-rd2-rd3-1997-2001.html

Hope it helps.
You have your work cut out for you.
Starter cut relay is just Honda's was of saying the starter relay
It should be in the under dash fuse box.
Oh, did you check to see if you have all the bigger fuses?
The bigger fuses can prevent the engine from cranking.
I know from experience. Shorted the damn thing.
Had to buy one from Ebay. Then, I got the bright idea to solder in the fuse
from another 80 amp fuse link into the gap of the blown fuse. Works ok.
Please keep us informed of your progress.