Please check the Media_* database tables and also the file system. If there are the records about the media files in the DB, then you just need to copy the physical files over FTP to appropriate folder on the server's file system. No export/import is required.
However, if there are no records in the DB, then the export/import should help - what were the settings? Was the option to export/import physical files selected? Is the folder structure of your media library the same as the target library?