I think the AC unit must be clogged up and allowing water to soak the carpets. Is there a drain plug or line on the AC unit or some kind of condensate drain line that may be blocked?
Wet Carpets on 2004 Lexus ES330
CHECKED THE HEATER CORE TO SEE IF IT IS LEAKING.IT ALSO HAS A DRAIN HOSE THAT ALOWS EXCESS WATER TO DRAIN OUT THREW FIRE WALL.
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I am almost certain there is a drain hose at the passenger foot well area at the bottom of the heater core/evaporator housing. If the condensation is not draining away it will wet the carpets. If nothing is found has your car been losing engine coolant? Perhaps have the cooling system pressurized to see if the heater core is leaking but this usually results in a slightly sweet smell in the engine compartment and the windscreen fogging up when on defrost mode.
Maybe someone else who is more familar with this car can chime in here to tell you better about the location of the drain, but the evaporator case is where the water will drain out of. I don't think this car actually has a hose but rather just a drain hole in the very bottom of the case under the hood against the firewall. You can probably better access it underneath the car.