My sons 99 A4 B5 is having some weird issues that I think have to be connected.
1) Power windows work without the key in the ignition both when the door is open or closed
2) Odometer lights up intermittently without the key in the ignition
3) Attempting to ulnock vehicle from inside the car will only unlock the drivers door. Same with using the key although if I hold the remote down (to unlock and somebody tries to open the passenger door, the passenger lock will slowly come up.
4) center lights of the instrument cluster do not work - all work other than those in the square section in the middle
5) slow battery drain - tried finding it with a multimeter and pulling each fuse and couldn't find the source.
It seems like a strange combination of symptoms and I'm not sure if they are all related or just some of them. I'm by no stretch a mechanic but typically I can figure this stuff out and I just can't get this one solved.

 

Weird electrical issues are usually because of loose grounds in the wiring harness. However, this case sounds almost like there's something shorting things out a little bit. Not enough to trip fuses and the like though. Have you checked under the carpet in the foot wells for water or signs of water entry into the car? Could be some stopped up drains letting water in.