Sounds like it's trying to import you data over the top of the sample data. i.e. all the tables already exist.

Your best best is to drop all the tables in the database that the new install created so you have an empty Db. Then try the import and it'll create all the necessary tables and add the data.

Alternatively, when you backed up your database, you get the option (checkbox IIRC) to DROP tables if they already exist and this puts all the necessary commands into the SQL file.

Hope this helps.