Installing a second WP blog in a sub-directory

I have a site at http://www.example.com, which runs a WP blog. Now, I’m planning to make a separate site that will, for the moment, be hosted off the same server. This will also be a WP blog, but using Pods.

I’ve created a new SQL database at my host and I have user settings for it. I’ve copied a new set of the WP installation to another directory, where I’ve edited the wp_config.php to reflect the new database settings.

However, when I go to http://www.example.com/secondblog/wp-admin/install.php to install this second blog, I get an error page from my regular site. How do I avoid this?

Might it be a problem with the directories? When I log into my FTP account, I have a directory called example.com. Inside that is data, log, public_html, sessions and a few more. I copied my new WP directory (“secondblog”) into this, is that right? If I put both secondblog and example.com in the very root directory, will both work and have the proper URL:s http://www.example.com/secondblog and http://www.example.com?