MySQLi and PDO result in "no such file or directory" error

I am trying to connect to my database using non-deprecated connection methods (e.g., using PDO or mySQLi in preference over mysql_connect).

No matter the method I use, I get a "no such file or directory" error (below). Most help on the web suggests to check the location of my mysqld.sock. I don't know how to do this without SSH...

How do I confirm the location of mySql.sock, verify that PHP is correctly configured and get mysqli or PDO to work on my shared hosting site?

Warning: mysqli_connect() [function.mysqli-connect]: [2002] No such file or directory (trying to connect via unix:///var/mysql/mysql.sock) in /path/to/my/script.php on line 16

Warning: mysqli_connect() [function.mysqli-connect]: (HY000/2002): No such file or directory in /path/to/my/script.php on line 16
Failed to connect to MySQL: No such file or directory

Line 16 is the connection (all variables are set to correct values):
$hostname = 'localhost';
$mysqli = mysqli_connect($hostname, $username, $password, $dbname);

OR very similar error occurs from code in the try block:

dsn = 'mysql:host=localhost;port=3306;dbname=mydb'
try {
$db = new PDO($dsn, $user, $password);
} catch (PDOException $e) {
echo 'Connection failed: ' . $e->getMessage();
}