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Have you checked engine compression, or timing yet? Most generally when the cam / crank sensor get out of sync (because the belt has jumped a few teeth or one isn't turning) you will have similar issues including erroneous fault codes relating to the camshaft sensor, crankshaft sensor, and often time ignition coil primary circuits.
A quick check would be compression, I would expect 175 psi +/- 5 psi or so.
2003 Jetta left rear window blue plastic part of the