Antoine,
While your goal of installing Moodle in such a way as to limit access to it to registered users only can certainly be accomplished, the error that you're experiencing isn't at all related to the folder in which you installed it.
Moodle is an application that is written in PHP and it makes use of many functions that are provided by the PHP interpreter on your platform that interact with an underlying database manager.
Judging from the error that you quoted, it appears that your site is operating on a Windows server, and that you were electing to use MS SQL as the database management system. However, the PHP interpreter on that platform needs to be equipped with some specific extensions that will support executing its database-related functionality with an MS SQL*Server. Evidently, this is not the case on that particular host.
Those necessary extensions to PHP can be provided either by re-compiling the PHP interpreter in such a way that the extensions are permanently included in its runtime image, or by providing the appropriate extensions as "shareable" modules which can be loaded and run when, and as, needed by the PHP interpreter. Details regarding those shareable modules will be included in the configuration file for the interpreter, which may be found in your file system under the filename "php.ini".
However, if your site is maintained on a shared hosting service, you may not have the necessary permissions to make the needed changes to PHP. In that case, you should contact your hosting provider, and explain your requirements to them. They may be prepared to accomodate your request as part of the services they provide you.
Hope this helps to clarify.
-- Paul