You mistake who the robber barons are. They are the ruling class not the business owners. Sometimes they get in bed with each other and the result is corporatism.
"Capitalism or market economy is that system of social cooperation and division of labor that is based on private ownership of the means of production."
A free market is merely what allows capitalism to work. If the market isn't completely free there is no capitalism. It is a form of socialism. There can only be two choices: capitalism or socialism.
We have never had free market capitalism in this country so we can not say it doesn't work. The problem you witness in the 19th century was a failure of government not of the market. The government failed to protect property rights and in some instances even instituted legislation to make it easier for certain businesses to do it.
The market does not act therefore it cannot fail -- nor does it aggress against individual rights. The market is merely a reflection of the many infinite choices made by individuals and interferences of government and other such coercion. In other words, it is only individuals acting in the market that "fail", the market cannot fail.