The "List Accounts" is what is needed to validate the connection, so it sounds like the connection details are simply not correct, or that privilege is not available via the API. You may want to take a look at their Reseller privileges from the root account as described in cPanel's documentation.
If you think the credentials are correct, you can update the module to disable the connection validation check, and see if you can create cPanel packages/services anyway. To do this, update /components/modules/cpanel/cpanel.php (line 1594 for v3.1.0 of Blesta) and change:
'valid_connection'=>array(
'rule'=>array(array($this, "validateConnection"), $vars['host_name'], $vars['user_name'], $vars['use_ssl'], &$vars['account_count']),
'message'=>Language::_("Cpanel.!error.remote_key_valid_connection", true)
)
to:
/*
'valid_connection'=>array(
'rule'=>array(array($this, "validateConnection"), $vars['host_name'], $vars['user_name'], $vars['use_ssl'], $vars['account_count']),
'message'=>Language::_("Cpanel.!error.remote_key_valid_connection", true)
)
*/