What do you want to import. Basically, the imports are the database and the tables. My advise is after you create the database in the Admin (I prefer from PHP code, in fact), then first export the tables from the older store to the new one.
This can be done
1. Open your older database
2. Click on export
3. it will ask you which tables and select all
4. click on export
5. Usually the mysql tables will be stored in /etc/phpmyadmin/
The file may have a format that looks like mysql_2011_12_09.sql
The file will be stored in phpMyAdmin folder.
Now, from your new database, click on the import and browse to the folder above.
Pls let me know if the above steps worked well.