Oh dear, I should have spotted that. Thank god Shrike didn't notice, that would have been three failures!
You must have no output before any of your session handling.
change your code to
<?php
error_reporting(E_ALL);
session_start();
isset($_SESSION['count']) ? $_SESSION['count']++ : $_SESSION['count'] = 1;
echo $_SESSION['count'];
?>
<br><br><br><br><br>
<a href=test.php>Increase the number!</a>
and see if that helps