Anonymous access is enabled in both central administration and on the site collection itself inside advanced permissions yet the site still is requiring a username and password. In IIS itself for the site both Windows Auth and Anonymous access are ticked. I would appriciate any suggestions on why the site is still requesting credentials.
Ensure that any page content to be served up is published/checked in (images, master pages, styles, etc).
Beyond that as long as anonymous access is for sure enabled in the application settings in central admin there isn't a whole lot for you to do (in SharePoint).