There are 3 flaps that I'm aware of: the EGR flap, the one in the middle of the crossover pipe, and one in the intake manifold where the crossover pipe connects. I would also closely inspect the engine for fuel leaks (around the IP and injectors). Another thought is the K40 relay which I had to replace because it was randomly shutting off my engine, but your symptoms are quite different so I'd try the easier and cheaper stuff first.

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2004 VW Jetta TDI (manual)

Past MB's: '96 E300D, '83 240D, '82 300D, '87 300D, '87 420SEL