Am I looking for something in CMS>Static Blocks in the admin backend?
You are right. The banner is added somewhere there. In order to make the system work when the module is disabled, it should be temporarily off.
All it shows for content in the home page is
{{block type="core/template" template="page/custom.phtml"}}
When I looked into custom.phtml, there seemed to be a lot of code regarding banners.
It's no good to load the collection in the template. You should move all this logic to the block.
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