It happened to me when I first installed FCP5 at home. I was given some HDV footages captured from my work place. As soon as I import those footage, I can only hear sound but with black screen. Then I compared everything installed by FCP on my computer to the one in the office, found two missing components in Library>Quicktime folder, AppleHDVCodec.component and AppleIntermediateCodec.component were the two missing codec in that folder. Never sorted out why it was missing during the installation. What I did actually was copied the components from the other computer and put in mine.
By the way, you can also try playing HDV footage with QuickTime Player (Pro), if you are seeing the same black screen with sound, then I think you are having the same problem as mine before I sorted it out.