Jan 29 21:39:24 Desktop cgminer[10849]: Testing pool http://api.bitcoin.cz:8332
Jan 29 21:39:24 Desktop cgminer[10849]: HTTP request failed: couldn't connect to host
Something is wrong with the URL. I am unable to access that URL from my browser, so maybe the problem is simply that the site is down. It is also a good idea to have a backup pool to mine. If cgminer has problems with one pool, it can automatically switch to another.