I see you are using Responsive Theme, I installed it on my test site to see how it works.
I'm having no problems swapping out widgets.
Looking at your source code - it appears you have an empty text widget in that empty 3rd widget area. If you remove the blank widget and put something else there, or fill in some text, it should appear.
The footer widgets are all Home Widget 1-3. The home widgets only affect the footer area, on the home/front page it would seem.
If you swap those out with something different, nothing changes? Sometimes if you change something and don't see it on your site right away, you need to press Ctrl and F5 keys at the same time to refresh your browser and see the changes.