The Internet is commercially funded and without any central governing body. The ARPANET was *one* of the predecessors, yes, and partly funded by the DoD, but also by UCLA, Stanford and two other unis. Its point was never to be the means to communicate after a nuclear war. That's just another myth and another example of your talking out of your arse. And it was actually closed down. There is a report floating around the interwebz about it.
There were a few European efforts as well, most with universities being heavily involved. And, of course, there was CERN whose scientists eventually came up with things like hypertext, the internet browser and HTML. The world wide web was born at CERN and was proposed by a British scientist, Sir Tim Berners-Lee.
TCP is about 40 years old, if memory serves. The IP address scheme that added that /IP suffix is a bit younger, I think. The Internet as a name is almost as old but gained widespread use during the 80s, especially at universities where you could access it. Then, of course, the Usenet was far more useful.
If the Internet was classified, it was the worst kept secret *ever*. But it wasn't. You don't know what you are talking about.