At first I was going to assume it may be a plugin/theme conflict. But when I went here:
http://claesmarkopark.se/wp-login.php
My web browser developer tools said the page was returning a 500 Internal Server Error. But I also went here:
http://claesmarkopark.se/wp-admin/admin-ajax.php
And that also returned a 500 Internal Server Error, when the correct response for trying to access the admin-ajax.php file would be a 200 OK from the server and I should have seen a “0” (without the quotes) in my browser. Since I should be able to access the admin-ajax.php file directly, that might indicate a different issue and not a plugin/theme conflict (of course I could be wrong if there is a plugin on the site modifying server configuration files like .htaccess, php.ini, .user.ini, etc.).
So I looked up the site at builtwith dot com, and it says the site is using WordPress 4.2 on PHP 7. If that’s the case, you’ll probably want to examine the site’s server error logs (especially the PHP error logs), as my initial guess would be that something on the site is not compatible with PHP 7. As WordPress 4.2 is quite old, and I believe PHP versions recommended at that time were 5.3 to 5.6.