This issue got to court because Circuit City technicians did a search on Kenneth Sodomsky's PC for video files and allegedly found child porn. He was charged but the trial court said that Circuit City shouldn't have done that. A Pennsylvania Superior Court disagreed and said that Mr. Sodomsky had no reasonable expectation of privacy after he gave his computer to the store for a hardware upgrade. Prosecuting pederasts is a good thing. For the rest of us, though, this may not be a helpful precedent.
An identity thief may merely need your name, your date of birth, and your social security number. If he has access to your hard drive, he probably has this and a lot more.