Creating a configuration Class in php
There is no need to make anything static here. I would pass the config file name in the constructor, and make everything an instance variable.
Any other object that needs configuration needs this config object, rather than referencing it via the singleton pattern
Storing the database configuration, like hostname, username and password makes sense in a config class. Actually connecting to the database does not.
Instead of using the die(...) function, throw an exception. Really, this would be made obsolete by not connecting to the database in a config class, but whenever you decide to do this, throwing an exception is more appropriate. You communicate that an insurmountable problem has occurred that you cannot fix, but you give other code in the system the option of fixing it.
The method names are in PascalCase -- idiomatic for C#, but not for PHP. The PHP Coding Style Guide from PHP-FIG is a good reference. Use camelCase instead, so LoadConfig becomes loadConfig.
The RequireFiles method isn't really configuration and doesn't belong in a config class. A class or function that has a more global scope in the application should be loading those, or take advantage of autoloading.