Ok! I figured it out.
First, there are two entries in the database that govern how the blog functions. The "siteurl" in the wp_#_options table refers to the backend system (well, most of it). It seems that the developer did not use the same methods to contruct the "view" and "backend" buttons under the Site Admin --> Blogs menu. This must be changed manually in the code (look for the wpmu-blogs.php file). Otherwise, just changing this field will make the rest of the backend switch to a new URL, or from http to https (as in my case).
The second entry is called "home" in the wp_#_options table. It refers to the frontend of the system, and changing it, will globally change (i'll so most links, but so far they all seem to work) links on the frontend of the blog.
I have hacked the code alittle, so that these values are placed into the database correctly. It's been awhile since I did this, so I'll have to report back if anyone wants to know.