There's nothing wrong with the links and with your robots.txt. But ...
You obviously have a huge duplicate content problem. Just look at the search result the site: query returns. There are a lot of old links (from the old CMS I suppose). Click through the links and you'll always get to the main page, but the URL remains the same. I.e. no redirect to the correct page with the new URL or to the Homepage.
You should have a look at your old URLs and redirect them with a HTTP 301 redirect to the new URL.
As a quick fix add a rel="canonical" tag to your new pages. This way google will index the correct page (and only the correct page) on its next crawl. Setting up the redirects should have happened prior to switching the CMS ...