As I read to your forum, the DNS seems to be the problem. But it is strange that when I rename the index.php file to index.php.old and create a new index.php which shows only a simple message, it appears correctly without ads!
The exact issue is that http://www.adelfotis-filioton.gr/ is working fine, but http://adelfotis-filioton.gr/ . Your wp-login.php page doesn’t redirect to the non-www domain, so it works. But the WordPress index.php tries to redirect people to the non-www domain, which is why you see the ads. This is probably caused by the Website URL setting in WordPress.
I’ve asked iFastNet to look into your domain name.