Like the OP, I have something similar happening on a couple of websites.
I think it has something to do with the way Google is selectively applying penalties to single pages, rather than entire websites.
The only way I can see this work is if the home page is triggering a non link related flag with the algo, good enough to ban the page, yet not the entire website. So the algo is left with all those "good" links pointing to the website, yet nothing to show, thus it simply pulls out the "next best" page.
OP - does your home page rank for anything at all?