I personally would consider more options vs jumping straight to the GM being the issue.
What happens if you try to lock the car from the exterior driver's door lock cylinder? Does the central locking system lock all of the doors/trunk/fuel filler door? Does it activate DWA (the anti-theft alarm siren) system and the red status LED in the clown nose below the rear view mirror starts to flash?
Remote/keyless central locking will shut down when there's an issue with one of the central locking system locking actuators. That would be all door lock actuators, the fuel filler door actuator, and trunk actuator. And since you said the interior central locking button isn't working (which is rare) then perhaps something is wrong, disconnected, or a fuse is blown. Have you checked ALL of the fuses for the central locking system?
Have you tried to simply reinitialize your remote keys, yet? If not...that's free...and if it works...you've saved yourself a lot of time and effort.
TIPS:
- KL R = ignition position 1 (not position 2 or 3 or engine running etc)
- make sure ALL doors are UNLOCKED
- make sure ALL doors are CLOSED
- only insert the 1st remote into the ignition...start the 2nd remote (like explained in STEP 3 & SETP 6) pressing the buttons as explained in STEP 3