I'm not totally convinced that you necessarily needed a new battery.
Clearly, there are two possibilities: Either the battery went flat overnight or it was already flat when you got back from the garage.
The battery could only go flat overnight if
(i) it was in such poor condition that 'always on' devices, such as the clock, took sufficient power to drain it, or
(ii) something was left on, such as the headlights, which drained the battery, or
(iii) there was something 'short-circuiting' the battery.
I would rule out explanation (i) because you would have probably experienced plenty of problems starting the car, over an extended period, if this had been the case.
I would rule out explanation (ii) because most modern cars warn you if you've left the lights on.
Explanation (iii) also seems to be unlikely. Short-circuits usually result in a fuse blowing, rather than the battery going flat.
That leads me to think that the battery was probably flat when you got back from the garage. The prime job of the battery is to provide the power to start the car. While you're actually driving, all of the power needed should come from the car's alternator. If the alternator isn't working properly, power is drawn from the battery instead, resulting in a dead battery by the end of the journey.
So, my guess is that the problem is associated with the alternator. It could either be that the alternator itself is defective (which is probably expensive to fix on an Audi) or simply that the belt driving the alternator is slipping. (If so, it's probably just a couple of minutes work, with a spanner, to fix it).
Chris