As per @Milo, I’m adding my comment above as an answer…
Try going to example.com/blog/wp-admin/options-permalink.php. That should work, because the php file actually exists. If so, try updating your permalink options to a friendly version, like “Day and name”. This will put a new .htaccess in the blog directory — I’m thinking that that new .htaccess will override the one in the parent directory.