To clear your old/problematic site from Google's cache (only), place
<meta name="googlebot" content="noarchive">
on EVERY page you want to get out of their cache. Then the next time Googlebot comes a'crawlin', your instruction will be received and those PAGEs will be removed from their cache. After you notice that Googlebot has visited, you can remove the META tag, above, from your pages, and the NEXT time Googlebot stops by, it will include the new version of those pages in its cache.
More instructions (from Google) can be found here