It is not likely the view finder is broken, because it is deep inside the camera. There can be many reasons why you can't use it as it should. Did you know you can adjust the brightness of the viewfinder and the display separately? It is in the manual page 31. And if you are with the manual (still online available) have a look on page 16 too.
When the camera does not give the image to the view finder, it also could be an electronic problem, because switching in the camera goes along electronic paths.
SOURCE: Black LCD screen and viewfinder in photo take mode
Sony (who bought KM) will fix this for free. http://esupport.sony.com/US/perl/news-item.pl?template_id=1&news_id=131
SOURCE: Screen and viewfinder only shows black....no picture
Are the pictures also coming out black? 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 the following for further info and a simple fix that may help:
http://camerarepair.blogspot.com/2009/05/simple-fix-for-stuck-shutter.html
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