I tried replacing the file, and got a similar error:
Warning: require(includes/initsystem.php) [function.require]: failed to open stream: No such file or directory in /home/teambrun/public_html/soccer-uniforms.com/admin/includes/application_top.php on line 126

So, obviously, you are right, this is not the fix. "Store-side files in admin?" I really do not know what this means. The site looks and works fine on the front, I just cannot get to the back. Sigh.