Hi I had the same problem you describe on my 1996 A4TDi, It turned out to be Ignition barrel. I'm not sure if that means the bit with the key in it or electric switch at end of barrel. (I had it fixed at garage so I don't know exactly but they said Ignition barrel, and its never given a problem since, the mechanic said it was a common fault). Hope this helps
Regards
Iain