The alarm should not stop you from locking/unlocking the doors. The chip only is in the car starting circuit and does not affect locking and unlocking the doors.
Is it possible the fob is from another car and only allows the car to start? You never know what someone sells you until you find it does not work.
The fact that the light appears in the red window on the fob just proves the fob batteries are good.
There are batteries available for the car and they will flash the lights and beep in sync with the indicator lights.
It is a good sign that the locks work using the console button, so the problem lies in the signals sent by the Fob or the signal receiver.
This receiver is behind the map light area I think, see if it looks like someone has played around in that area.
I am no expert by any means on this subject though. Pizzaguy may know the answer hopefully
Good luck..