Deciphering the language of monkeys and apes

You most likely have come across apes using some form of language that they learned from humans. Koko communicates with a set of symbols.  Washoe, Nim and other chimps were taught sign language.
Scientists are still finding evidence that monkeys and apes in the wild are using different calls to identify various things.  The howler monkeys (see video link below) announce themselves with a loud scream to dissuade anybody who might even think about going into their territory.  Most monkeys have alarm sounds they use to warn the rest of the troup when a predator is nearby, so everyone can run to safety.
Yet, humans have not been able to crack the code that would allow our species to communicate with other primates.  Is it because primates lack a language as such?
In an article published in the NY Times on January 12, St Andrews University (Scotland) Dr Klaus Zuberbühler confirms that monkeys have specific sounds for specific situations or predators.  Campbell's monkeys in Ivory Coast have even been observed to add suffixes or prefixes to change the meaning of calls.  Baboons are able to recognize the sequence in which sounds are heard and attach a different meaning to them based on such order.
However, it seems (as of now anyway) that primates may lack the ability to really communicate (by adding more information such as the distance of a predator to their location) because of wiring in their brains, according to Marc D. Hauser, animal communication expert at Harvard.

Deciphering the Chatter of Monkeys and Chimps - New York Times - January 12, 2010

Howler monkeys sounds - National Geographic

Vervet monkey alarm call

Study of capuchin monkey alarm calls