Featured Image and Archives Not Working Since 3.8 Upgrade

A client’s site: https://group92.com was working great before the 3.8 upgrade and now both the featured image on new posts and the entire archives are not working. It seems that both are referring to incorrect file paths. For example, the January 2014 archive folder is pointing to: https://group92.com/2014/01 – which doesn’t exist.

Help! I have spent hours going over this to no avail. It’s running a Cherry theme which says that I need to upgrade, but I will loose all of my customizations (again, hours worth of work with no promise of solving my problem). Has anyone found a fix for this?