I don't think the format or settings have changed; otherwise you wouldn't be able to log in with your old computer. It sounds more likely that you are failing to properly log off from an FTP session, and have some number of open sessions at your IP address -- don't just close the client, but make sure you do a "logoff" or "exit" from the menu. See if that helps. You may have to do this several times before the extra sessions are closed.
If you've been using the old computer for a long time, and letting it log in for you with stored ID and password, it's possible that you've misremembered the ID or password (if they don't show up in clear text). See if you can get the FTP client to show you everything (including passwords) in plain (visible) text.