I own the "non-free" version of Object Dock, and it is behaving exactly the same way. I believe that the vendor/developer (Stardock/???) included a hard coded Internet address or DNS name in the product(s) and the information service provider (AccuWeather) has changed the way they distribute the information needed, or just plain blocked access from this product. The "Internet Not Available" message started in the last day or so.
Accordingly, this begs the question, when will Stardock address this issue with a FREE update for the Weather docklet?