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Thanks for the feedback.
This is Tim with Microsoft Office 365 SharePoint Support.
Adding a Silverlight web part should not have changed your ability to view your public-facing website. Would it be possible for you to provide me with your domain so that I can try to browse to your public-facing website so that I can see if I am getting prompted for a username and password?
I will continue to monitor this thread and wait for your reply.
Microsoft Office 365 SharePoint Support