How to install WP alongside my existing site at a sub-directory (bradydjohnson.com/blog)?

Could you be more specific about the issues you encountered? Have you tried the following?

  1. Creating a database for WordPress (if you haven’t yet).
  2. Copy the WordPress core files into bradydjohnson.com/blog.
  3. Load bradydjohnson.com/blog on your browser to run the WordPress installation.