I had this problem in my wife's 2000. You can fix the problem yourself with a little patience. The drain tube is not findable by looking under the car, it's on top of the exhaust behind a heat shield.
1. Remove the passenger seat. (Two bolts at the base of the front seat and three wiring harnesses)
2. Remove trim around carpet and seat belt anchor.
3. Remove glove box.
4. Peal back the carpet and drain the water out of your TCM first (black box-open it) if it still works at this point. You should take it out and dry it in a bag of rice.
The drain tube is between the center console and the glove box way up in the corner where it is almost impossible to get the carpet out of the way. There is one bolt that will allow you to pull it from the hole in the floor/firewall and clear it. Some people have a clog, some folks have had the exhaust melt the end shut. Use a vacuum to suck out the tube.
Leave the carpet up and drain the spongy material. I tied the carpet up to the "oh ****" handles up top and let it air out. Leave it up long enough to drive the car around a few days to make sure this fixed the problem. I have had every single water issue available to this model car. It sucks.
This is my last Audi.