My Nikkor AF-S 55-200 no longer works in autofocus mode. Camera is Nikon D40X; other lenses still autofocus, and this one used to, but it just stopped. Yes, I have made sure that the switch is set to "A." When it is, nothing happens; I can set it to "M" and manually focus, but there are times that I really need autofocus.

Lens mount Nikon F mount (with AF coupling & AF contacts)

Lens compatibility • D-type / G-type AF Nikkor (except IX-Nikkor): Autofocus and all functions possible
• PC Micro-Nikkor 85mm f/2.8D: Usable in Manual exposure mode
• AF Nikkor other than D-type (except AF Nikkor for F3AF): All functions except 3D Matrix Metering possible
• AI-P Nikkor: All functions except 3D Matrix Metering and autofocus possible
• IX-Nikkor: Cannot be used
• Non-CPU: Usable in Manual exposure mode (exposure meter cannot be used)
Electronic Rangefinder usable with lens with maximum aperture of f/5.6 or faster.

Sorry, but the D40x lacks an autofocus motor, depending on the lens to have one. Nikon calls such lenses AF-S. This particular lens does not have such a motor, relying on the camera to have one. The only 50mm lens currently available with an autofocus motor is this one:
http://www.nikonusa.com/Nikon-Products/Product/Camera-Lenses/2180/AF-S-NIKKOR-50mm-f%252F1.4G.html

Earlier this week the Nikon web site listed a new 50mm F1.8 lens with an autofocus motor, but then it was removed. Hopefully they will officially announce this lens soon.

There is no such thing. You can see a full list of current Nikon lenses at
http://www.nikonusa.com/Find-Your-Nikon/Camera-Lenses/index.page

You can see a list of current and old Nikon autofocus lenses at
http://www.bythom.com/nikkordb.htm

You'll see that no 50mm Nikon lens has ever had VR.

Make sure you set the aperture ring on the lens to its smallest setting (largest f/number) and lock it. Without doing so, the lens will not communicate properly with the camera and thus you will not get the autofocusing.

Hi,
Sorry to hear about your lens. If you are able to autofocus and take pictures with any other lens, then it means that your problem lies with the kit lens. If you can take picture in manual mode, but not in autofocus mode, then the AF motor in the lens in not functioning. I had the same thing happen to my 50mm 1.4 lens.
Depending on your location, there are Nikon repair centers in Melville, NY and Torrance, CA.
Hope this helps,
Andrew

Your motor may have gone bad. Try sending it to PhotoTech Repair Service in NYC. They are Nikon authorized, and can do the repair under warranty if you still have it. Also if you join they're facebook page, they will give you a 10% discount.
Here is the facebook page link, it has everything you need to send it in.
http://www.facebook.com/pages/New-York-NY/PhotoTech-Repair-Service-Inc/102527215194

Is the switch on the side of the lens set to manual or auto? Sometimes it's the little things like this that we don't notice.

You need AF-S or AF-I Lenses. These have the autofocus motor built in to the lense. The D40 and D40x does not have an autofocus motor in the camera body itself, while the D80, D300, D3 Etc to have the motor in the camera. You can use most old lenses on your D40x, but you will have to focus them manually.

See Ken Rockwells page for a lot of D40 / D40x info
http://www.kenrockwell.com/nikon/d40.htm

Try removing the lens and then reloading it.   Hope this works.

Here is Nikon's specs of lens compatibility for the D40X:


Compatible Lenses*: Nikon F mount with AF coupling and AF contacts Type G or D AF Nikkor:
1) AF-S, AF-I: All functions supported;
2) Other Type G or D AF Nikkor: All functions supported except autofocus
3) PC Micro-Nikkor 85mm f/2.8D: Can only be used in mode M; all other functions supported except autofocus
4) Other AF Nikkor*â¹/AI-P Nikkor: All functions supported except autofocus and 3D Color Matrix Metering II
5) Non-CPU: Can be used in mode M, but exposure meter does not function; electronic range finder can be used if maximum aperture is f/5.6 or faster
6) IX Nikkor lenses cannot be used
*â¹ Excluding lenses for F3AF

They do not recommend 3rd party lenses, ever