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Unfortunately you cannot achieve this by editing your Site CSS. I'm afraid it's not possible to add a link to the banner image. A workaround would be to use a Style template without a banner area, and add your banner in a Picture Widget at the top of the page. You could then add a link to this image.
However, your Page Heading is clickable, and will take people to your home page by default.
I'm sorry I cannot offer you a better solution for this at the moment.