Finally got it, my problem was in wp-include/post.php, due to bad translations of the queries from MySQL to SQL.
I had to replace code in wp_insert_post function with this code:
if ( empty($post_date_gmt) || '0000-00-00 00:00:00' == $post_date_gmt ) {
if ( !in_array( $post_status, array( 'draft', 'pending', 'auto-draft' ) ) )
$post_date_gmt = get_gmt_from_date($post_date);
else
//$post_date_gmt="0000-00-00 00:00:00"; changed by because sql doesn't like empty dates
$post_date_gmt = $post_date;
}
if ( $update || '0000-00-00 00:00:00' == $post_date ) {
$post_modified = current_time( 'mysql' );
$post_modified_gmt = current_time( 'mysql', 1 );
} else {
$post_modified = $post_date;
//$post_modified_gmt = $post_date_gmt; changed by because sql doesn't like empty dates
$post_modified_gmt = $post_date;
}