car cuts out

It's the Check Engine indicator. Probably lights up yellow, somewhere near the center of your instrument cluster.

Sitting without a battery, weird things can result. At this point, I'd use a VAG-COM or similar to dump codes to see what might pop out, then clear all codes and re-adapt the ECU and TB and see what happens. If you don't have access to same, it might be time to visit someone (mainline dealer) that can do it for you.

btw, no chance you just have a crapload of condensation accumulated in the fuel tank?