There is a small lever mounted on the hammer face, called a "strut." If it is stuck in the rearward position or has been removed, the action would work as you describe. Dribble a couple of drops of solvent (and no more) down the hammer face after cocking the hammer and see if it starts to work. It may just be dry and need some lubrication.
Colt did make some Officers Model Special revolvers with single-action mode only, but they have a short cocking stroke that's a dead give-away. The old King Gunsight Co. in California made a similar conversion, but in that case the revolver should be so marked.