Well, thanks again, everyone, you guys were really helpful. I used either the Avira Antivir or the Avast program first, and whatever one it was worked ok, but I used AVG second, and I liked it better.
It found 526 threats, none of which were mislabeled or even slightly ambiguous as to whether they were malware or not. My neighbor was just fortunate that he only had dial-up, or the malware/trojans/etc. would have spread even worse.