The D40x only autofocuses with the latest
AF-S (and old professional
AF-I) lenses. Most
traditional (screw-type) AF lenses from 1986 through today will not autofocus on the D40x. If your lens says "AF-S," you're fine.
Most lenses sold today for the D40x are AF-S, and so is the included
18-55mm kit lens. Many non-Nikon lenses from Tamron, Tokina, Quantaray, Sigma and anyone other than Nikon still won't autofocus on the D40x. Try before you buy, but honestly, there isn't much the included 18-55mm lens won't do.
Autofocus systems are fast, but not usually instantaneous. You have to hold the shutter down halfway as you compose the first shot so the AF system can focus and lock, and then the camera fires instantaneously when you press the shutter the rest of the way. See
Preventing Shutter Delay for more.
What do you mean by "the shutter button won't depress." It physically won't move, or when you push it, it goes down but does not take a picture? The lens may be damaged (not hard to do) or the contacts may still be dirty. It may not be seated all the way. Does the lens release click when you mount the lens onto the camera? Is it a standard or VR lens and is/are the switches fully in one position or the other.
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