It sounds like a mechanical problem within the tumbler.

There is a mechanism that allows only one 'start' cycle. The key has several Positions: Pos 0 (Off) Pos I (Accessories on) Pos II (Run/Pre-Glow) Pos III (Starter) The key returns by spring from Pos III to Pos II when released.

Diesel starting procedure involves a pause at Pos II for pre-glow, gassers do not need a pause.

From Pos II the key is turned to Pos III to start, but once the key is released, it cannot be turned from Pos II to Pos III again until the key is turned all the way back to Off, resetting the lockout. This prevents embarassing starter grinding on an already-running engine. Been there, done that!

This is common practice with German vehicles, your Golf may be similar My Audi had the same feature.

I don't know the inner workings of the tumbler, but it sounds like the reset didn't happen. Perhaps not turning the key all the way back, perhaps a sticking mechanism, perhaps a broken spring...

Proper lubrication might work, with careful wiggling to reset the lockout, or else replacing the tumbler as has been suggested.

Best Regards,
Jim