My similar vintage passat needed a new ignition switch. Never thought to install a starter button, though i should have! I got a new switch from GSF for a fiver or so.
I would think that shorting a live to earth would blow a fuse before actually damaging any wiring.
If the engine runs even for a moment that would seem to indicate the ignition system, ECU, etc, is OK.
Perhaps like the fuel pump is priming but not pumping when engine is running? Do you hear the priming sound when you turn the key?
You might need to get yourself some wiring diagrams...
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