I have experienced a true hangfire. I was shooting a borrowed Remington 1849 Pocket Model. The mercury had played havoc with the nipples, and I touched off one round only to have a "click" of the falling hammer. Maye ten seconds elasped with a little smoke curling from the cylinder area, then the gun fired.
Replacement nipples were hard to come by in those days, so the owner made do with what he had.