While I'm not an attorney that would be the best person to ask this question of, we do have a lot of cases that have both criminal and civil implications...
I would say that the Salvation Army store would probably not be liable as they are not under obligation to protect a previous owner. In my opinion it would be like trying to sue a car dealership for failing to remove a social security card of the previous owner from the glove box. The original owner failed to protect himself and then likely lost any claim to action against anyone else.
Unless of course the store stated that they would "prepare" the systems to be ready for new owners by wiping them clean.
Even though they might not be liable, it's still sad that the manager wouldn't allow a few extra minutes to try to get rid of the personal info. Most people are ignorant of exactly how much they are giving away when they dispose of an old system.