If it is happening each time you boot up then there is a programme trying to run at startup. Go to Start and look for Run, click on it to open up a box and type msconfig and hit Enter. Look for the Start Up Tab in msconfig and untick the box that mentions Microsoft LifeCam. Click OK and you will be asked to re-boot. Next time you boot up with a bit of luck the black screen won't come up.
Then check with your communications programme (Skype or whatever) that your LifeCam is still working OK.
The msconfig trick does not fix the problem but it does stop it from happening on boot up. This link click here might help you understand what I have suggested.