Assuming you have checked the battery is around 12V, other possibilities are faulty starter motor (or solenoid), but this would not have caused the engine to stop while running. So, if you can rule out a seized engine (not likely, but possible, even if you have the correct oil quantity, if the oil pump fails or pickup is blocked). Did you see the oil pressure warning light up at all? For a seized engine, I would have thought you would see an oil pressure warning before it croaked.
If none of the above, then possibly electrical...so immobiliser or ECU. For this you need a VAG COM. If you don't know anybody with one, cheap option is buy an OBD2 USB cable from eBay for about £10 - £20, it should come with a shareware copy of VAG COM (you can download it also).
Just thought of another thing, might sound dumb but not sure how the immobiliser works, try using the spare key to start it.