Before we check out your admin area, can you go to your Menu Manager area and let us know what type of link you're using for your Home Page? What component is setup to be displayed. On your home page, I see a banner area and then some navigation modules in the bottom.
It doesn't look like a component is being displayed. Is there an article or something else that's supposed to display there?
Again, I'm pretty sure you simply don't have your component output enabled, and my guess is that it's in your template that that is disabled. Without knowing your site or extensions, I may not be able to figure out what's happening even with admin access. It's best if you can investigate where the component output is, and if it's not displaying, why not.
Thanks,
Alex