Why would you want to have a background picture for all your SharePoint pages? That is an awful user experience. SharePoint is a collaboration platform for sharing documents in document libraries and using lists to manage data. Why slather company branding over all SharePoint pages?
Have you customized Word and Excel to show that background image on every page, too? I thought not. So why would you want that in SharePoint? It's a tool for collaboration. Give it a few custom colors, but then leave it alone.
If you are really intent on pursuing this, the Site theme and icon are not the way to go, as you have found out.
You will need to use SharePoint Designer to either inject custom CSS into your pages or customize the Master page of your site. This will not be a simple check box, but will require a good understanding of CSS and how SharePoint 2010 CSS works.
But I really strongly, STRONGLY advise against that idea.