Autofocus will not work,

Make sure the A-M switch on the lens is set to A for autofocus.

Also make sure the AE-L button is set to on (pg 144 of your manual) in your menu's otherwise the half-press of the shutter won't allow it to focus.

Use autofocus if you have a AF lens on it.

Usually you get a kit 18-55 AF lens that has a A/M switch on the side. The switch should be facing the A side so it's set on autofocus. Then you have 9 points on your viewfinder, those are the autofocus points. It should usually be set to center, because you usually want the object in center of your photo to not be blurry.
Remember to press the shutter button halfway and give some time for the autofocus to focus. Then you can press it all the way, you should have your photos nice and clear.

If you happen to have a manual focus lens, you should be watching through the viewfinder and turning the focus ring on the lens and determine if your object is in focus. It's hard at night, but get some practice at home when you have some more light so you get more familiar with the focus.

Do you have access to another camera? If you do, try the lens on that camera. If you get the same results, it's the lens. If no, then it's the camera body. Once you isolate the problem you'll know if you need to get the lens fixed or if you need to get the camera fixed.

you should change the focus lock to AF-S, instead of AF-C

Check your Custom Setting Menu, a1-a10:AUTOFOCUS.

Press Menu, select the Custom Menu Setting (looks like a pencil).
Select "AUTOFOCUS" and move to right.

a1 AF-C Mode Priority. Set to "Focus"

a2 AF-S Mode Priority. Default is "Focus", change this to "Release". This will enable the camera to fire anytime you press the shutter, regardless of if it's in focus or not. Use this setting if your having problems locking up, especially using some different lenses.

Try these settings. They may work for you.

hello, mount another lens and check? this will indicate if the the problem with body or the the lens? check if af is on?
look if the mirror has got misaligned, if it has got slightly misaligned fire the shutter at slow speeds this will set it right.
hope this solves the problem

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.

Is your shutter speed fast enough? If not, you'll need a faster shutter speed or a tripod.

Are you using the proper focus sensor? Is the entire image blurry or just portions of it?

What happens if you focus manually? If it comes out sharp, then there's a problem either with the lens or the autofocus system on the camera. Have you tried it with a different lens?

Is the AF switch on the lens set to A?

You might like to check if the A/M slider switch on the lens by the Nikon label is set to A.
It sometimes gets moved accidently.
Set to M the lens will not autofocus.

"... Autofocus Lock ("AF-L"). Pressing the AF-L (Autofocus Lock) button enables the Nikon F4 to lock the focus. Simultaneous lock of AF-L and AE-L is possible. "'FREEZE FOCUS" - is another great function in the F4. It allows automatic shutter release when subject enters a pre focused distance - available with Nikon MF-23 and/or the 250 exp. MF-24 Multi-Control Back. i.e. with the shutter button fully depressed, the shutter is automatically fired when a subject comes into a preset manually focused position. This function is recommended for sports races because the racing course is usually known beforehand. It also works well in wildlife remote control photography, scientific, forensic and other technical photography. ..."