My DSLR shows a vignette in photos when the lens is extended

You have to zoom the camera lens out for that lens to work.

Try tapping gentley the beck of the camera or helping the lens to extend by pulling them with your finger nail, see if this can unlock the lens gears.

If you camn get the lens to extend, the problem is solved

not a easy fix. when it is not connecting it defaults to the widest aperture so it is letting in as much light a possible. you could try speeding up your shutter speed and see if your start seeing a image

Sound like the focus screen and frame fell out

Never, never touch the mirror!!!. You have dust on your sensor. Google the words "how to clean a DSLR sensor" and you will find sites which explain the procedure and places to get the supplies needed.

You don't. The D40 works as SLRs have worked for half a century. Only more recent dSLRs (Nikon started with the D3 and D300) have the LiveView capability that lets you handle your dSLR as a point&shoot.

Try pressing the power ON and when the lens has retracted, remove the batteries. Wait a few minutes. Press the power ON again. Now replace the batteries and try the camera again.

Try these procedures.

Lens errors are fairly common. Usually it's sand or grit interfering with the lens extension mechanism. Or the camera's been dropped with the lens extended. Or the camera has been powered on, but the lens had been blocked preventing its extension. Or the battery ran down with the lens extended ...

Here's some things that you can do to try to correct it. They only seem to work for less than 50% of the lens errors, but if the camera is out of warranty, they're worth a try:

http://camerarepair.blogspot.com/2007/12/fixing-lens-error-on-digital-camera.html

I sent my camera back to Fuji and they replaced the CCD free of charge. I had the same problem plus sometimes the pics just came out completely white