Inside the Ejector rod there is a center pin that gets pushed against the Bolt, which then moves it back to free up the hammer. This center pin is pushed back by the front locking tab under the barrel.
From your description, something has gone wrong along that chain of parts.
1) The spring for the front lock may have failed or it may be jammed in place by fouling. If this tab doesn't drive the center pin to the rear, the failure is exactly as you describe.
2) The center pin may be bent, peened, or damaged in some way so that it cannot move freely. It could also be gummued up by old dried oil or fouling. The result of this is that same as what you've described.
3) The bolt may be jammed by debris or gummed up with old dried oil. With the same result.
Problem is that this all depends on a balance of forces that are exerted by relatively small springs, so poor maintenace or years or disuse can cause problems just like you have described. The good news is that in most cases, a simple thorough cleaning is all that is needed to get it working properly. Some indoor shooting ranges offer ultrasonic cleaning as a service for a fee. If you have a range that offers this near to your homestead, all you may need to do is remove the stocks and have them drop it in the cleaning tank. After that, a couple of drops it the right spot is all you'll need to do to have it shooting well for years.
As for removing the sideplate and pulling the lockwork for a complete and thorough cleaning, it's not at all difficult provided you have properly fitted screwdrivers, remember to tap the sideplate loose and not pry it, and have a rebound slide tool to make installing the rebound slide easy.
As for taking the ejector rod out of the cylinder, also easy, however you will need to know the year of production for your gun. In 1960 S&W reversed the thread direction from right hand to left hand threads. In addition, to protect the extacor star you'll want to load up the cylinder with fired casings to help distibute the torque and minimize the chance of damage. In addition, getting those threads engaged properly after a disassembly is a matter of "feel", they are a very fine pitch and easy to cross thread. What I found worked best for starting the threads was to push against the spring tension and spin the knurling in the unscrew direction until a very light click is felt. That click is the threads dropping into engagement and the ejector rod with then spin in easily between thumb and forefinger. NOTE, if it doesn't spin in freely, you've got it cross threaded so back off an try again. BTW, it took be a full 50 minutes to get it right the first time, now I can do it in seconds. I've found an old bit of leather belt folded over the knurling at grasped with pliers works well for both loosening and tightening without leaving even a hint of a mark on the knurling. Also, for tightening, use one hand as a "slip clutch" by grasping the cylinder while you tighten the ejector rod. If it shoots loose, grasp a bit harder next time you tighten it. As for firmness of that initial grasp, think firm handshake to a Line Officer, not a stupid firm challenge you might give to a Marine Boot. Finally, NEVER USE LOCKTITE, you'll just gum it up and lose any chance of feeling the threads engaging properly, in addition when properly tightened they won't ever shoot loose.
Note, a Kuhnhausen S&W Shop Manual should be considered a MUST for any wheelgunner. Most of the common tasks required to service these revolvers is actually rather simple once you start doing it. However, one warning is that you should do the first few in a large ziplock back because some of the springs can go zinging off like tiny rockets if you don't know what to expect. I'll also warn you to be careful when removing the trigger to keep the hand in place, that particular spring is notorious for being rather fussy to re-install. I also don't fool with the sear on the hammer for single action, it's nearly microscopic and the result of tinkering with that is usually months waiting and looking for a replacement hammer. In fact, I don't do anything to the single action sear on the trigger as long as it's not pushing off, a lighter rebound spring is a much safer method for reducing the SA trigger pull and minimizes the risk of push off developing.
Finally, if you just don't want to do this yourself, I can think of no better place to send it than S&W. They have a superb reputation for restoring the function of these guns to better than new condition and know all of the tricks for getting it perfect. Downside is that non warranty work seems to run to a 2 or 3 month turnaround. However, they do offer an expresss service for a premium and I suspect that if you contact them and tell them you are currently Serving, you may get that express service for free or at a discount.