To elaborate on 2jdtbone 's post:
The long pin that holds the cylinder in place is called a base pin.
On the old 3 screw (non safety conversion) pistols the end of the base pin is just a rounded end (2 pins on the left in the below image)
On the newer single actions and the converted 3 screw models the base pin has a small plunger in the end of it (3 pins on the right)
The pin serves to push the transfer bar (sliding bar that covers the firing pin when you pull the trigger) out in order to clear the firing pin.
If this pin is missing or you happen to have the old model base pin in the gun the transfer bar will hang up on the bottom of the firing pin and exhibit the symptoms you describe.
Parts 3,4, and 5 in the image are the base pin latch. This is there to hold the base pin in the frame and keeping it from backing out under recoil (not too large of an issue on a single six). While I have heard of some base pin latches getting buggered up, those are mostly on the 45 colt and 44 mag Blackhawks and Super Blackhawks as a result of heavy recoiling loads.