Shutter won't open/close, and blank screen on "capture."

Not sure if you mean the automatic lens cover, or the actual lens shutter, so here's fixes for both:
Stuck automatic lens cover
Stuck shutter

A stuck shutter is another common failure mode for digital cameras. 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.

A stuck shutter is another common failure mode for digital cameras. 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.

A stuck shutter is another common failure mode for digital cameras. 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 happens to own a SD1000. Great little camera, but it's prone to stuck shutter every once and a while. Easily fixed each time though by simply opening the battery door while on, and gently flicking the lens barrel a few times. Again, see the link.

Theirs oil on the shutter blades causing it to stay closed, Thats why you can't see though the lens or the viewfinder also, This comes from the grease from the zoom assy, It's a major job to fix it, Has to be fixed by a repair shop

First try pressing the DISP or DISPLAY button to make sure that you didn't accidentally turn off the LCD. But if that's not the case...
Try taking and downloading a picture taken while the screen is blank. Is the picture also blank? If so, a stuck shutter is another common failure mode for digital cameras. 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, 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. Read the users comments there also for more tips.

Do the icons show up on the screen or is it totally blank?
Can you view previous pictures?
If the icons show on the screen then have a look into the lens to see if the shutter is closed over the inner lens. you may have to adjust the zoom to bring the inner lens and shutter mechanism up close to the outer lens to get a better look.
If the shutter is covering the inner lens then it is stuck and will need to be freed by opening the camera up.
If the screen is just black then it just may be possible that the ribbon for the screen has partially slipped out of it's socket on the main board.
If it comes out all the way then the camera should not even power up.

A stuck shutter is another common failure mode for digital cameras. 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, 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.

A stuck shutter is another common failure mode for digital cameras. 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, 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:

http://camerarepair.blogspot.com/2009/05/simple-fix-for-stuck-shutter.html

I think you mean your automatic lens cover opens. A stuck shutter is a common failure mode for digital cameras. 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, 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 the following for further info and a simple fix that may help:

http://camerarepair.blogspot.com/2009/05/simple-fix-for-stuck-shutter.html