6v6gt:
Oops. You're right. I didn't look carefully enough.
But if the regulator has failed, but not shorted, the Nano should still work if powered by the USB. If the Schottky diode has failed the Nano should still work if powered via Vin. (If I read the thing correctly now, that is).
All depends on what happened after the initial failure. If the regulator died short-circuit Vin to Vout, and 12V was later applied to Vin, all sorts of damage could have happened. That's why I said earlier: "The whole Arduino isn't destroyed at that stage, just the regulator."
If the regulator failed short-circuit to ground, connecting USB would short the 5V to ground.
I think they'd need a careful examination to see exactly what's failed.
If the regulator failed open-circuit, then you're right, the board should work when powered from USB, but the LED would no longer light since there's no longer a current path back to Vin.
There are a few possibilities.