Can cops hack into your computer without your knowledge?

YES absolutely. However normally the only law enforcement agencies that have ALL the capabilities to do that are the FBI and CIA. Microsoft "claims" that the reason you have to register Vista and Windows 7 online is to combat software piracy, but in fact, it allows Microsoft to scan your PC whenever, and also to allow the FBI or CIA into your computer under the guise of looking for terrorism. They do this through a "back door" that is placed on your computer and law enforcement and Microsoft are not the only ones who can figure out how to exploit the back door. This "right" they have to invade your computer without your knowledge is granted to them by the patriot act.

And I don't care if you don't like George Bush, whoever edited my answer to delete Bush's name has no business doing so. So stop editing my answers. If you don't like the truth, find another line of work.