"However, on the family PC, which still has the AOL browser software installed, I can login using my password,"
so you have a password stored on that PC which is NOT what you think it is. The AOL software is logging on with a changed password
You should be able to discover it using this tool
Mail PassView: Password recovery for Outlook, Outlook Express, Thunderbird, Windows Mail, and more... the download link is
http://www.nirsoft.net/utils/mailpv.zip
disable your antivirus software before unzipping and running it. Its a safe program, but most AV programs freak out over it
As for support, the free AOL accounts are handled by AOL USA not UK> Theres an international premium number to call them listed somwhere on the AOL help website