A stuck shutter is another common failure mode for digital cameras, particularly for the SD1000. The symptoms of a stuck or "sticky" shutter are very similar to CCD image sensor failure. The camera may take black pictures (for shutter stuck closed), or the pictures may be very bright and overexposed, sometimes with lines, especially when taken outdoors (for shutter stuck open).
To confirm a stuck shutter, put the camera in any mode other than "Auto", and turn the flash OFF (you don't want to blind yourself for the next step). Next look down the lens and take a picture. You should see a tiny flicker in the center of the lens as the shutter opens and closes. If no movement is seen, then you likely have a stuck shutter. If so, please see this link
for further info and a simple fix that may help.
By the way, my wife's SD1000 also has this problem every once in a while. I easily fix it by using the following steps from the link: powering on the camera, opening and closing the battery door, and
flicking the end of the lens barrel with my fingertip (or you can tap it with a pencil as discussed in the link).