Only one start attempt allowed

[Radek]

Hello Audi-fans;

The car is my son's 2000 A6 2.7 biturbo.  As of lately, the car allows only one start attempt at a time.  In other words, it starts and runs fine, but once switched off, it will not start again unless the battery gets disconnected for at least 30 seconds.  It cranks fine but feels like it's not getting gas.  It was quite awkward around town, at every stop I had to lift the hood, disconnect, wait a bit, put it all back - several times during the day.
Another observation I made is that the car does not have to be actually started to induce this behaviour.  Turning the ignition "on", like to enable to open the windows, and then "off" triggers this behaviour - the car would not start again without disconnecting the battery.

It vaguely points me to the Crankshaft or Camshaft Position Sensors, but perhaps someone can point me to the problem before I start taking things apart.
Thanks.

Radek.