New MK7 GTi Owner - Unresponsive touch screen, faulty ambient light etc

[Lordie]

Whatever the warranty says, a garage cannot sell you a car with a defective touch screen.
You should insist the garage sorts out the problem, whether it's a software or hardware problem ( sounds very much like the latter to me)

The problem is that the garage sold me the car with an AA Gold Extended Dealer Warranty so I'm not sure if this means this is the only warranty I have or that that is on top of the actual warranty the garage supplies too.

Very have always been very friendly, professional and helpful so I guess the best bet is to try contacting them to see what they say 

[Yusee]

The warranty is irrelevant. They have sold you a car with a significant defect. I would strongly advise you not to accept the car ( and not to even attempt to fix it yourself)- it could cost you thousands to replace a touch screen.
I would be pretty firm with the garage- write or email them to say you will not accept the car with a major fault, and unless they agree to fix it, you are rejecting the car.
When you first posted, I thought you had bought a cheap car privately. If a garage has sold it to you, your approach has to be quite different- the law will be very clearly on your side