Site not displaying correctly with www. in the URL after moving site to new server

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Hey everyone,
I just finished moving a clients site to a new dedicated server and everything works fine except when I change the site.php Base URL to include the www. in the URL the site breaks, meaning that the theme disappears along with all styles, the content and images are still there, they are just scattered throughout the whole page.

When I switch it back to the URL without the www. it all works fine and the whole reason I need to change it to include the www is for SEO purposes but mainly because the client cannot view the website without the www due to their network securities.

Any help would be greatly appreciated as this is mind boggling??