I got this lens (Nikon AF NIKKOR 50mm f/1.4D) for my D3100 and it doesn't autofocus. I don't knowhow to intervene since there's no switch on the lens itself (because I understand it is small and it doesn't have a motor) but I think the body should be autofocussing, but I press the shutter button half way through as usual and nothing happens. I have bad eyesight so it's a pain for me to focus manually.

There are a series of small brass "buttons" on the outside bottom of the lens where contact is established. If a new lens, there may be some dirt or grease on them preventing contack. Wipe lens and camera buttons carefully with a lent free cloth and retry. Then it is time to go back to the seller.

That lens will work with the D3100, except for the autofocusing. In order to autofocus with the D3100, you need AF-S lenses, such as the AF-S VR Zoom-NIKKOR 70-300mm f/4.5-5.6G IF-ED or the
AF-S DX NIKKOR 55-300mm f/4.5-5.6G ED VR.

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.

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

yes. http://www.nikonians.org/nikon/slr-lens.html

The lens has an autofocus motor, but because it is an older model, it will not autofocus for the D40(x), D60, or D5000, which have more stripped down components. I advise you exchange the lens for the newer model, or return the D5000 and get the D90 for just a bit more.

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.

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.