The problem is your brand links are filters, not categories. Filters filter the list of products being displayed. There are no products on your front page therefore there's nothing to filter.
The other problem is that products of those brands exist in many categories. So if you click a brand filter, what category is it supposed to load?
If you want your brand filters to load the search results page, then you should change your links from this:
<li><a href="[server.url type='fullpage' query='brand=Adidas']">Adidas</a></li>
<li><a href="[server.url query='view=search&brand=Adidas']">Adidas</a></li>