If you have trouble importing large database dumps (.sql) files into PHPMyAdmin, the alternative is to upload it to your FTP root and use the SSH command line to import it. Before importing the database, make sure you have created it in cPanel and assigned the user all privileges. The command to import the database is:
mysql -u user_name -p database_name < dump_file.sql
After you hit the Enter key, you will be asked for the user's password. Type this in and press Enter again, the database will be imported. You can go in to phpMyAdmin to check it has been imported correctly.
This is done through an SSH application. One that we recommend using is Putty. You can download this for free at http://www.chiark.greenend.org.uk/~sgtatham/putty/download.html (Download the Putty.exe file.)
Host field is the domain name, make sure SSH is selected. Login as: use cpanel user name and the password is your cpanel password.