Three things come to mind that have plagued us before.
SSL
301 redirect
.htaccess
If all these do not match, you will not be able to log in to the admin. Since you made changes while logged in, this is where I would look.
Make sure the SSL points to the same as in the two config files. Nowadays most just drop the www in favor of the non-www URL. Regardless, if your SSL is for
www.your_site.com, then the two configs should have www as well. Reverse for non-www. Both server listings should be https:// and true for SSL.
Make sure a 301 direct does not exist that takes you away from the correct URL. There may be an old 301 at hostgator or in your cpanel (Redirects under Domains) that takes the admin away from the proper, secure URL.
Same goes for the .htaccess in the root of the site.
Once they are all matched up, you may just be notified that you need to change your password due to going https:
BTW, you won't find anyone here on the forum who advocates using the "one click installers" provided on many hosts. While they might work for a small-, initial-installation, they more often than not create a problem from lack of files.
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