Hi D, welcome to the forum. Sorry your intro is a lemon. Most of the S&W products are superior items. That's no comfort, but your case is unusual, despite what you may hear.
I think there's an issue with the cylinder stop, stop spring, or possibly even the trigger. I have no idea how much you know about the innards and how they work, so in the interest of covering it just in case:
The stop stays in the up position all the time, held in place by a small spring, and locking the cylinder from turning. When the trigger is pulled, a "lip" on the forward edge pulls the stop down, unlocking the cylinder and allowing the hand, which is also attached to the trigger but on the other end, to turn the cylinder to the next chamber. That forward part of the trigger slips off the stop very quickly after the trigger pulls it down, allowing the stop to "scrape" or slide along the surface of the cylinder until it hits the stop indentation for that next chamber and stops the turning. I think the stop spring is either damaged or even missing. Not sure, but definitely related to that stop piece.
Again, glad to have you here. Most of us are heavily into the S&W brand, products and history, so if there's pretty much anything you're interested in S&W-wise, someone here likely "wrote the book." Best of luck with your firearm.