The box_news_id field of the box_news table is defined as an auto_increment field (see /admin/includes/init_includes/news_box_manager_install.php):
Code:
// ----
// Create each of the database tables for the news-box records.
//
$sql = "CREATE TABLE IF NOT EXISTS " . TABLE_BOX_NEWS . " (
    `box_news_id` int(11) NOT NULL auto_increment,
    `news_added_date` datetime NOT NULL default '0001-01-01 00:00:00',
    `news_modified_date` datetime default NULL,
    `news_start_date` datetime default NULL,
    `news_end_date` datetime default NULL,
    `news_status` tinyint(1) default 0,
    `news_content_type` tinyint(1) NOT NULL default 1,
    PRIMARY KEY  (`box_news_id`)
)";
... as such, that field has an implicit MySQL-calculated default value.

I'll suggest that you review the structure of the box_news and box_news_content tables via phpMyAdmin to ensure that the structures match that installed by the module referenced above.