Hello, I hope the following assists you.
Although the carpet appears dry this is due to the fact the sound deadening absorbs all the water that comes into the car.
The first thing to check is the door(s) on the driver's side. The doors are designed for water to run inside it and out of the drain holes at the bottom. Make sure the drain holes are clear. With the aid of an assistant stay in the car while water is poured on the door, look for any signs of water coming from the bottom of the interior door trim, if the weather shielding behind the trim fails or has a hole in it water can come through and run behind the trim then drop from the door into the car.
Another point is if the car has air conditioning when this is turned on make sure condensation from the heater assembly is draining underneath the car, if the drain tube is blocked condensation comes from the heater assembly through it's joints into the car.
The only way to thoroughly dry the carpet and sound deadening is to remove the seats then the carpet. If there isn't a leak from the doors or heater then having the carpet removed will assist finding the water ingress, the big problem is water travels through the sound deadening so the water can drop in the front but as the deadening becomes saturated it will be soaked all the way to the rear.
I hope this helps, let me know if I can assist further and I'll reply as soon as I'm able to.