I can think of 2 things for you to check out. ECU uses the D4 light as a 'check-tranny' light, similar to the check-engine light. (Dunno if VW does this??) AutoXoned can plug in an OBD-II reader & read the error code, if there is one stored.

There's a starter interlock involved with the shift lever. Clean it all up down there, there should be a switch assembly which tells the system which gear it's in. If that's flaky, the system 'thinks' it's in D4, & it interrupts the starter circuit.