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Does your PRNDL display on the dash show the correct gear you have selected, or are they all highlighted? You may need to check the TCM box under the passenger side floor to make sure there is not water entry into it- pull the kick panel, and lift the carpet enough to pull out the black plastic box and open it up.
Normally the PRNDL display will show the gears in black on a light background, but the selected gear will be highlighted as a light letter surrounded by a dark background. If you have an issue in the system, it will "highlight" all of the gear selections. You will need to have the transmission control module scanned for faults. Many auto parts stores will do scans for free, but many of them have "generic" scanners that will only read the engine, not the transmission or any other modules. You need someone with a factory scan tool, Ross-Tech VAG-COM software, or a good Snap-On or other scan tool that can read all modules. Otherwise, without an obvious issue like water under the carpet, you are just guessing and throwing (expensive) parts at it.