Sir Aardvark's proceedure is pretty much exactly what I do. Brake cleaner is functionally the same as gun scrubber and easier to come by cheaper (auto parts store).
His procedure will fix about 98% or more of all "new to me" older S&W problems. Per Mountain Bear's instructions, check that the rebound spring is not cut-down too far. I opened a 1942 Navy Victory last weekend and found this inside:
Yikes. This is what you want it to look like after a careful cleaning and judicious specks of grease or oil on the working surfaces:
However, before you dig into it and disassemble your gun, you may want to check this - remove the mainspring screw from the front of the grip strap (it is the one behind your ring finger in a shooting grip - if your grips cover the front strap of the grip frame, take them off and you will see it). Unscrew it and check the end to make sure it hasn't been filed down, and that it is securely screwed in all the way.
If you do dig into it, you can also remove the rebound spring/slide without buying the dedicated tool from S&W. I find a cheap 3/32" punch with a tapered tip works great. Removing isn't the problem (except possibly loosing the spring as it shoots out; be careful), it's installation. With the tapered punch you can use it to hook the spring end on the retaining post in the frame very easily, then pop the slide all the way in. Saves getting a $20 specialized tool good for nothing else:
Lastly, check that spring is not cut to short. This one had been - as you can see the ends are snipped and it only has 12 full coils. It should have 15.
Before you go inside the gun, read the sticky near the top of the Revolver forum, he walks through the proper way to get in there without doing damage. Very nice post by member Sylvan_Forge.