Please double-check your SMTP settings. The problem is much more likely to be related to your SMTP settings than anything like the location of your Showkase site/Contact page or your browser or internet connection.
Depending on your SMTP settings, you might need to set SMTPSecure to either 'ssl' or 'tls' by adding a line of code such as the following:
$mailer->SMTPSecure = 'ssl';
... or:
$mailer->SMTPSecure = 'tls';
You might also need to ensure that the 'From' address is a valid email address on your domain.
Try changing line 91 from:
$mailer->setFrom('mailer'.strstr($siteEmail, '@'), $userName);
... to:
$mailer->setFrom('your@email.address', $userName);
Hopefully, checking that all the required SMTP settings are being used and are correct will solve your problem.
Otherwise, I'm afraid you might not be able to use the Contact Form within Showkase on your web server.
As I mentioned earlier, the Contact Form within Showkase officially requires PHP mail support and other methods are not supported.