PHPMailer + Gmail - No route to host (113)

SMTP -> ERROR: Failed to connect to server: No route to host (113)
SMTP Error: Could not connect to SMTP host.
My code is (note some things sanitized for public viewing):

<?php
   $paths = get_include_path();
   set_include_path($paths . PATH_SEPARATOR . dirname(__FILE__) . '/phpmailer');
   include_once('class.phpmailer.php');
   $mail = new phpmailer;
      
   // Constant email settings.
   $mail->IsSMTP();
   $mail->SMTPAuth   = TRUE;
   $mail->SMTPSecure = "tls";
   $mail->Host       = "smtp.gmail.com";
   $mail->Port       = 587;
   $mail->Username   = "--@noas.com";
   $mail->Password   = "--";
   $mail->From       = "contact@noas.com";
   $mail->FromName   = "NOAS Contact";
   $mail->WordWrap   = 75;
   $mail->Subject    = "10th Anniversary Dave Thomas Celebrity Cookoff - Chef Invite";
   $mail->AddReplyTo("--@noas.com", "--");
   $mail->IsHTML(true);
   $mail->addBcc('--@noas.com','--');
      
      $mail->SMTPDebug = 2; // For debugging, change to 0 when working
      
   foreach( $emails as $info ) {
      $mail->AddAddress($info['email'], $info['name']);
      $mail->msgHTML(buildmsg($info['name']));
      
      // Send mail message to each recipient
      if( $mail->Send() )
         $content .= 'Message to '. $info['name'] .' sent successfully.<br />';
      else
         $content .= 'Message to '. $info['name'] .' failed to send.<br />';
      
      $mail->clearAddresses();
   }
?>

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<?php
   $mail->SMTPSecure = "tls";
   $mail->Host       = "smtp.gmail.com";
   $mail->Port       = 587;

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SMTP -> ERROR: Failed to connect to server: Connection timed out (110)
SMTP Error: Could not connect to SMTP host.