I've had a *similar* problem to this, and there's one check you need to do to tell if it's the same problem -
When trying to restart, does the glowplug light come on?
If it DOESN'T, replace relay 109.
My problem was that if the car was run for a few minutes then stopped, it wouldn't restart. However, I didn't have the oil light coming on!
A good source of info for this is the US site tdiclub.com - that's where I learned about the relay 109 problem, while VW dealer could only say "It doesn't show us a fault code", which of course means they can't fix it!
Read here -
As to the air in the system theory, it *could* be -
- an air leak into the fuel line (check for loads of bubbles in the clear line to the injector pump. Some is OK, though)
- running it dry has dragged a load of dirt up the lines and clogged the fuel pump. also worth draining the fuel pump, in case it's full of water - often missed at service time.
The bosch injector pump on these engines is self-priming, and recirculates fuel back to the tank constantly - unless there's an air leak or blockage, it should sort itself out in a matter of minutes, and shouldn't recur.
My money's on relay 109 though - a sub-?20 part from VW.
PPS - If you can solder, you can fix it for 2p! Pop the relay open, and resolder all the joints.