If you only have a SQL database of your old WordPress account, then you should be able to transfer the site given you have access to the cpanel.
WordPress SQL Transfer Steps:
1) Create a New Database
2) Create a New User and associate with the Database (add all privileges)
3) go to phpMyAdmin and IMPORT old WordPress Database
4) go to the WP_OPTIONS, make sure the "option_name" - "siteurl" points to the correct name for the WordPress
5) Take note of the WordPress PREFIX, something like WP_ or alike. One database can contain multiple WordPress databases.
6) Use the File Manager or FTP and edit wp-config.php, the following DB_NAME, DB_USER and DB_PASSWORD (see steps 1 and 2)
7) Also, check the $table_prefix to match
8) now you should be able to login to wp-admin.php
9) update the database if needed, then change the Permalinks under Settings. Make sure to hit "Save Changes", even if nothing has been changed, the database will be updated.