I would guess that the action is gummed up with old lubricants, and this is causing the cylinder stop to malfunction. Dry firing of S&W rimfire revolvers is not recommended.

A good internal cleaning with your favorite solvent, and re-lubrication with some light oil may take care of the issue and restore the proper function of the cylinder stop. (check the integrity of the cyl. stop spring and the other internal parts)
The cylinder assembly may also need a disassembly and thorough cleaning.

When checking the action, be sure to take care not to dry fire the gun under mainspring tension with the sideplate off.

You might also have a look at the firing pin to see if it is undamaged.

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Ret. LE, FA Instr, S&W Armorer