Question for computer nerds

I put this on my facebook and I know some of you are on there but some aren't.

This isn't happening to me this time haha, but its happening to my gf's parents. We went to their house the other day and I gave them a new moniter. When we were making sure it worked the computer was already on Amazon. We went to search for something and noticed someone elses email address was logged into Amazon. We checked it but there were no items being bought so we just logged off and figured maybe it was just a name from whoever owned the computer before. Today they got 2 emails saying that their passwords were changed on ebay and when they turned the computer on it was already on ebay but no one went to the ebay website. Is this a case of someone using their computer through their IP address? If so how do you stop it? They aren't using Wifi so someone isn't using it through that. Any ideas?