Do you have Access to PhpMyAdmin? Most cpanel powered server has it. you can export the database from there.
You will need the database username, password and database name. After you ssh into OLD server, type "mysqldump -u USER_NAME -p DB_NAME | gzip > FILE.sql.gz" Enter the database password when it asks. Then, usinf FTP or sFTP, copy the FILE.sql.gz file from the OLD server to the NEW server. (Presumably by copying it from OLD server to your PC and then to NEW server.) After you ssh into NEW server, type "gunzip < FILE.sql.gz | mysql -u USER_NAME -p DB_NAME" Enter the database password when it asks. When it is done, your database will be copied to the new server. PM me if you need more help.
It's actually rather easy to do through ssh: Login to old host: Commands: First, dump the database to a file. mysqldump database -uusername -ppassword > database.sql then open an FTP session to your new host: ncftp -uuser new-host then put the file dump on the new server. Navigate to any appropriate directory first: put database.sql Exit twice, first to close the FTP session, and the SSH session: exit exit ssh to new host (make sure the database actually exists!) mysql database -uusername -p < database.sql or simply mysql database -uusername -p enter password source database.sql by: Web Hosting Talk