Try this method and don't forget to create backup of everything including the theme files and database. Try to consult a WordPress developer before doing anything.
1. Login to wp admin panel, go to Settings -> General page and change values in 'WordPress Address (URL)' and 'Site Address (URL)' from 'new.domain.com' to 'www.domain.com'. Press 'Save Changes' and don't pay attention to errors that may appear
2. Connect to the server via FTP, create new folder in the root dir (ie. 'oldsite'), put all files and folders from the root dir (except folder with wp) into this new folder.
3. Move all files and folders from the wp folder to the root dir.
This method is advisable if your stage server is within or a subdomain of your live site.