There is an electrical connector under the carpet and lining that gets wet. Simply drying out the connector will not solve the problem since the connector actually corrodes. You need to peel the carpet back, locate the connector, open it, clean the terminals, pack with di-electric grease, and re-connect. Some dealership techs will even go to the extent of sealing the entire connector with heat-shrink tubing and sealing the ends with automotive-grade silicone.
There are a multitude of problems that can happen with a bad connection. You have only touched on a few but I've seen many more experience more complicated issues. Consider yourself lucky! Good luck with the repair.
~Andy