The first click on a Colt Cap & Ball revolver is the trigger snapping forward to engage the "half cock" notch of the hammer. The cylinder locking bolt started pulling out of the cylinder notch as soon as the hammer started to move and by the time this first click happens, the cylinder locking bolt should be totally clear of the cylinder, allowing it to turn.
The second click is the sound of the cylinder locking bolt snapping back against the outside of the cylinder just shy of the locking notch in the cylinder.
As the hammer is pulled back further, the third click is the sound of the cylinder locking bolt snapping down into the locking notch in the cylinder. Once this happens, the cylinder can not be rotated.
The forth click is the sound of the trigger sear entering the full cock notch and the gun is ready to fire.
If the cylinder doesn't turn freely after the hammer has been raised from the fired position to the first click, there might be something wrong with the locking bolt or with the cam that is on the hammer down inside the frame that is keeping the locking bolt from disengaging from the cylinder.
Perhaps disassembling the grip and trigger guard from the frame and applying a light coating of oil to the inner workings of the gun will fix it?
Also remember, the gun is built to be cocked in one smooth motion from the fired position to half cock and from half cock to full cock. If you stop anywhere between these positions and lower the hammer, it can cause things to not work like they should (like, locking the cylinder when it should be free to rotate).