All done… you can change the radish image I used in the WP header to what you want. I also installed two plugins:
1. Dynamic Widgets – this let’s you publish widgets where you want on select pages, etc. I used this for your widget with the banner image
2. Remove Widget Titles – This lets you have titles on your widgets but hide them by adding a ! just before the title (see your banner widget title I did)
So right now, you have the widget with the banner on every page except the front page and vice versa. If you don’t want the widget image on the other pages, simply delete it then and keep the WP header one.
The reason why it was not showing is because the banner widget you were using was overriding it. Another reason why I installed Dynamic Widgets so I could publish the widget elsewhere but the front page, in turn, the WP header now shows there.