When you say the trigger can be pulled, do you mean all the way, or just a small amount? It seems to me that this might be the sear on the trigger missing, as that could cause the hammer to barely move, and nothing else, as the rebound lever works the cylinder stop on these. If this is the case, and if the cylinder stop is holding the cylinder from revolving, then working the trigger will grind the cylinder hand against the ratchet until it skips, so it's not good to do this much, or you'll need a new cylinder hand, or possibly have to fix the ratchet on the cylinder.
Below is how the triggers sear to hammer works.
Colt Sear 2 by
matneyw, on Flickr