2002 Volkswagen Cabrio starts & cuts off

car starts right a way, runs for one second then cuts off?

Will it restart and run fine after this? Will it continue to run if you floor the accelerator? I wonder if your fuel pump is going bad and can’t maintain enough fuel pressure…if it’s the original pump it’s 16 years old now

Is the anti-theft light flashing?

On some cars, if a valid key isn’t recognized, the engine will run for a second or so, then the pcm will cut the fuel

Do you have another key to try out?