Check the error log of your HTTP server (e.g. Apache). In 99% of cases of a blank page, PHP has experienced a fatal error and exited before generating any output.
If this script works on another server, I'd check that the script can find everything it needs to include or require. Files not found are common fatal errors when moving a script from one environment to another. For instance, if you deployed the file to the new server without configuring the include_path correctly.
Re your comment about the notice you got:
Notice: Undefined index: submit in /var/www/admin/index.php on line 8
the function on line 8 is if($_POST['submit'] == 'Login')
This means your $_POST array does not contain a field 'submit'. Referencing a non-existant array index in PHP is an E_NOTICE. You can fix this in the following way:
if (array_key_exists('submit', $_POST) && $_POST['submit'] == 'Login')