No need to PM the domain. This is an issue with LinkedIn being very picky with it's widgets. When you created your LinkedIn application, you gave it a Javascript URL. That URL for your site was with the www in it. That means that the social widgets will only work that very specific URL.
The LinkedIn Share button actually doesn't require an API key, but if one is provided, it goes into that restricted mode. All the other widgets (Company Profile, Member Profile, etc) as well as authentication do require the key though. I'm assuming you need one of these functions.. in that case you'll need to setup a redirect on your site from the non-www version to always go to the www version. If you're using an .htaccess file on your (Linux) server, you can add the following code toward the top (after the RewriteEngine On setting):
RewriteCond %{HTTP_HOST} ^example.com
RewriteRule (.*) http://www.example.com/$1 [R=301,L]
Hope that helps, but if not, let us know!
Alex