Hi Jtiffin,
You should definitely hear a click. Yes, put the correct key in the keyhole while it is glowing red. You won't actually see the key enter the hole -- just hear the click.
After using a key, right click to release it back into inventory before picking up the next key.
Also (this is important!) - be sure that you have the colour coded paper in your inventory which gives you the clue for opening the door. To get this, you have to left-click on the numbers painted on the ceiling in the water tunnel, and Carol will note them down.
The door will open automatically when all the keys have been correctly used.