To clarify, you hire some (really expensive) people who start by prying the computer apart and making a copy of the hard drive(s). They then go through it, looking for interesting stuff in files (Word documents can contain previous versions, for instance), in the browser history, in unused parts of the drive (i.e. for deleted files), etc. There is no "operating the computer" in the conventional sense involved: using the computer would destroy evidence (i.e. overwrite deleted files).
In cases like this, I'd imagine one would have an obligation to respect the owner's privacy (except where relevant to the case) - dragging all his/her porn into court is not exactly classy.