How much power do Mexican drug cartels really have?

I was reading this article about the dumping of 35 dead bodies on a road in a Mexican city. In addition to this piece of news I often read about the warring drug cartels and the police and other protective services seem unable to even curb their activities. I also am aware that unless you live in a certain country, the news can give you a distorted, one-sided view of the situation.

So I want to know how much power do these drug cartels really have? Do they influence (bribe, threaten etc) the government and law enforcement agencies? How powerless is the government against them?