Cannot stay logged in to Admin area - bad SSL configuration

I am running v1.3.8a. I have not upgraded since the site was created, about a year ago. My SSL certificate was just updated, and after that, my entire secure folder seems to have been deleted, so I re-uploaded the files from the http side to the https side.

Now I can access the admin page, but when I try to move beyond the main admin page, I am re-directed back to the admin log-in page.

By following this tutorial page:
https://www.zen-cart.com/tutorials/index.php?article=281
I have been able to determine that the problem is bad SSL configuration, as changing ENABLE_SSL_ADMIN to 'false' lets me log-in, and the admin page works perfectly.

However, when I take a look, my configuration files in includes/configure and admin/includes/configure are consistent with the tutorial on enabling SSL (https://www.zen-cart.com/tutorials/index.php?article=14).

I am at a total loss for how to deal with this. Can anyone offer any advice/ possible options for troubleshooting?