I copied in all the files, cleared the cache folder and set the proper permissions. When I go the the phpbb_seo/phpbb_seo_install.php page, I am met with a login screen and after logging in, I see the install welcome page. Clicking ANYTHING on that page takes me back to the same login screen. What's the problem here?

Please help before I go crazy!

Try logging into administration control panel first and then start the installation of phpBB-SEO.
If this doesn't work try using: /phpbb_seo/phpbb_seo_install.php?mode=install_phpbb_seo&sub=final

I tried both suggestions....same loop to login screen

By the way, this was an installation on a forum I had already started setting up. I didn't really get too far so if I have to start all over, I guess I could.

Just a guess, but maybe the cookie isn't being set (?) correctly. Your cookie_domain in the phpbb3_config table should be something like '.example.com' (without quotes and with a leading "."). The cookie path is typically "/" (again without quotes).