Unknown part in ignition assembly

I had the ignition cylinder go bad in my car that I just got like 2 weeks ago. I got a new one from auto parts store and ordered a switch at the same time. When I removed the cylinder and replaced it with the new one, nothing happened when I turned the key except that the key moved to start the car position. But that was it. I could turn the key on and off, but it wouldn't start the car. So I removed the new cylinder and looked inside the housing trying to come up with what might be wrong.
On a when I grabbed the needle nose pliers and reached inside the housing to see what the thing was inside there that had a little nub like thing facing out towards me, see if it moved at all or if it was stationary or what. When I grabbed it, it pulled out easily and so I took it all the way out. Well, it was broken. So, there was my problem!
I looked at the new cylinder and nothing like it was on it, so I just figured it must be something that comes with the new switch. I was wrong. It didn't come with either the cylinder or the switch.
In fact, no one seems to know what it even is. Including more than one local auto parts stores. So I have included photos of it in hopes maybe someone can enlighten me so I can fix my darn car!
Just so you can picture where it was and how it was in there, the little nub thing I could see inside the housing after removing the cylinder, is on top of the flat round piece.