mysql_connect("localhost", "db_user", "db_password") or die(mysql_error());
			mysql_select_db("db_name") or die(mysql_error());
			$result = mysql_query("SELECT * FROM db_table WHERE region like '%$region%'") or die(mysql_error());
			$num_results = mysql_num_rows($result);
			if ($num_results == 0)	{
				echo '<br />';
				echo '<p>There were no matches in the database for your search criteria';
				echo '<br />';
				}
			while($row = mysql_fetch_array($result)){
			echo '<br />'.$row['result1'];
			echo '<br />'.$row['result2'];
			echo '<br />'.$row['result3'];
			echo '<br />'.$row['result4'];
			echo '<hr />';
			}

Solution - 1

Hey, Are you trying to connect to the localhost or some external server database? Here's the code that worked for me with both connecting to localhost and remote database.

$db1 = mysql_connect( 'localhost', 'db_username', 'db_password' ) or die( mysql_error() );  
$sel1 	= mysql_select_db( 'db_name' ) or die( mysql_error() ); 
$query = "SELECT something FROM some_table";
$res1 = mysql_query( $query, $db1 );
while ( $array = mysql_fetch_array( $res1 ) ){
	print_r( $array );
}

Solution - 2

Is the second database in the same server where your wordpress is installed? if not, you must allow this IP (where wordpress is installed) to the mysql server. suppose, ur wordpress is installed in 192.168.1.1 and your mysql server is installed in 192.168.1.5 then you need to allow 192.168.1.1 in your mysql server. you may write the following statement in mysql console: >

grant all privileges on `db_name`.* TO 'db_user'@'192.168.1.1 ' IDENTIFIED BY 'db_pass';

Solution - 3

if your user have same credentiols for assecign db its a simple. 1)

//second db name
define('ONEMOREDB', 'clients_tartak_tartak_ua');

function queryresults() {
	global $wpdb;
  	// no `` in db query for db table name
  	$result = $wpdb->get_row("SELECT * FROM ".ONEMOREDB.".tartak_news as news LIMIT 1");
	var_dump($result);
	exit;
}

add_action('wp_head', 'queryresults');

define('ONEMOREDB', 'clients_tartak_tartak_ua');
add_filter('query', 'sql_filter');

function sql_filter($sql){
	if (strpos($sql, ONEMOREDB.".") !== false){
		if (preg_match_all('/`'.ONEMOREDB.'\.([a-z_0-9]{1,})`/si', $sql, $m)){
			foreach($m[0] as $match){
				$sql = str_replace($match, trim($match, "\"`"), $sql);
			}
		}
	}
	return $sql;
}
function sql_results_test() {
	global $wpdb;
	$result = $wpdb->get_row("SELECT * FROM `".ONEMOREDB.".tartak_news` as news LIMIT 1");
	var_dump($result);
	exit;
}


add_action('wp_head', 'sql_results_test');