It sounds like your server's configuration for DirectoryIndex does not have index.php specified. So it does not load it. I assume you are using Apache. The DirectoryIndex directive tells the server which file to serve if no file is specified such as when typing your domain name or a folder.
So try putting this in your .htaccess file:
DirectoryIndex index.html index.htm index.php
If no file is specified, the server will load index.html, index.htm, or index.php if they exist.