I picked up a 410 a few years back. Near perfect condition. This was a much later model.
Think the reason it was in such great condition is because it would not fire. (In addition, it would NOT close when loaded. I had to take some material off the extractor face to get it to do so. This was after trying multiple different brands of ammo).
Turns out, the hammer face was contacting the action before it could make contact with the transfer bar. I compared with a hammer of another gun of similar vintage, and it had quite a bit more material on it. Exchanging with the other made it functional. I ended up having to remove some material from the hammer face to make it work. The gun must’ve been made with Friday afternoon parts.
Anyway, try the hammer spring first. Not sure if your “vintage” of gun has a transfer bar system, but something to look at, if it does, to make sure hammer can make good contact with it.
Also, what Hookeye said is KEY. Use a “slave pin” to re-assemble. You can use drill bits to function as slave pins, if you don’t have something else. Assemble with the “slave pin” (loose fit), then chase it out with the real pins, that will have to be tapped in lightly with a hammer.
