The link you provide is to a free hosted WordPress.com blog and if you are logged into WordPress.com and nothing happens when you click a like button or try to leave a comment that indicates you have a browser related issue.
If you are not running one of the browsers and versions listed at http://browsehappy.com/ please try upgrading or switching first.
Note: If you are using an IE9 browser in compatibility mode that makes it render as IE7 and IE7 is not supported. To disable see > http://www.sevenforums.com/tutorials/1196-internet-explorer-compatibility-view-turn-off.html
If you are running one of the browsers and versions listed at http://browsehappy.com please do these four things:
1. Try clearing your browser’s cache:
2. Make sure that you have third-party cookies enabled: http://en.support.wordpress.com/third-party-cookies/
3. Try with all browser extensions or add-ons temporarily disabled.
4. Try enabling HTTPS: http://en.support.wordpress.com/https/
If it’s still happening, let us know exactly which browser (and version of it) you’re using by checking here if necessary http://www.whatbrowser.org/ and also post any error reports you get.