Firstly, use these settings for Google:
$mail->IsSMTP();
$mail->Host = "smtp.gmail.com";
$mail->SMTPAuth = true;
$mail->SMTPSecure = "tls"; //edited from tsl
$mail->Username = "myEmail";
$mail->Password = "myPassword";
$mail->Port = "587";
But also, what firewall have you got set up?
If you're filtering out TCP ports 465/995, and maybe 587, you'll need to configure some exceptions or take them off your rules list.