Have you looked at Moodle cloud? Free moodle hosting that will allow you to restore your course.
The short answer to your question is that you do need a web server - you don't need to publish your site to the world but you need php and apache to get it running.
If you install is failing at git, just download the current code from the downloads section and copy it to your www folder. Create your moodledata folder and database and then make sure that you have correct permissions set. Look at the directions linked to.