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.