When I had a Touareg there was a trick to reset your automatic gearbox - it doesn't cost anything so might be worth trying.
Basically you put your foot flat on the accelarator, ignition (not engine) on and hold pedal down for 15 - 20 seconds. Then foof off and start it up.
If your battery has been flat it might have caused various errors - this might help reset the ECU/ECM - as an aside, if it's th original battery, then even if you fully charge it, it may already be a goner especially with all of the cold weather.