This is an electrical problem. Probably related to the round, multi-pin connector located at the transmission, drivers side, near the lower portion of your transmission. This is the connector that most of the control data is sent through. The other possability is that the TCM (trans. control module) is getting a false signal from the "multi-position selector switch" or it's connector. This is the switch that is directly connected to your gear selector (left side, rear/center of trans.) and reports the gear selectors postion to the TCM. Without the correct input to the TCM, the TCM, does not know what signal to send to the valve body assembly.
Begin (if the vehicle can be driven safely) by taking your car to a reputable transmission service center near you. Before you go, call and ask if they have "VAG com. software". They will need this software to check the function of the "multi-position selector switch" and verify the inputs to the TCM.
As mentioned in a previous post, water migration into the TCM, has been a serious problem for these vehicles. Audi settled the class action lawsuit related to the problems. So, it should not be overlooked.
Hope this will get you started.

 

I have a different problem with my A6, mine is not as goofy as this, but the trans switch (multifuction switch), is very very pricy and to replace it you gotta get the mount off the trans, my car intermittently wont start and the dealer was telling me that before I throw 650+ at the switch that I need to have the cable adjusted, this may be something that applies to you as well, It does sound like you need to go after the module, and all applicable connections regarding the trans but if werent aware of it there are a couple of things that can be done before spending a ton more money