Tracing the real history of the Internet is a little like telling who the most important people where in the 20th century-- you will get a different answer from different people. Although generally agreed upon major players and organizations make it in to most stories of the Internet, you will find derivations from the source material that depend on, well, the source! The Brits, French and Americans all think they did something major to help develop what would eventually become the internet. But frankly, one thing should be said that is not normally expressed in most text books or fact lessons- the Internet itself was not a pre-planned notion or idea. No one woke up one day and said "hey, we have computers. Let's build a world wide connected system of redundant path communication nodes, with a robust protocol and extensible architecture." In fact, most of what we now have that is used on the Internet was an amalgamation of ideas and systems that merged over time, to meet the needs of different governmental and commercial entities.
For me, as a software engineer, I began using the Internet in 1993. One thing commonly minimalized by "Internet" historians are two major points: 1) popularization of network services to home users by the CompuServe service (the first true precursor to the modern day ISP). 2) the explosion of the Internet directly attributable to the development of the Mosiac Browser and the work done at NCSA-UIUC. Frankly, most "historians" tend to think technology drove the Internet explosion. But that is short sighted. We had connectivity technology long before 1993/1994. But no one really cared much about it (except scientists, academics and military minds) before the release of the Mosaic browser. Mosaic was the grand-daddy of all web browsers. From it, all browsers came. Once we have a graphical viewing tool to accompany the information storage and retrieval devices of the internet, common use of the web exploded- and Internet found a lifeline to become the predominant technological and commercial wonder of the last 20 years. These two points (CompuServe and NCSA-UIUC's Mosaic browser) are often trivialized by historians, because, frankly they see the non-academic/scientific influences as being somehow less valuable. But they are crucial. Keep that in mind as you read or watch any history of the Internet.
For those who want a somewhat extensive (and less than clearly scholarly) review of the Internet development, I would refer them to the well-kept article at Wikipedia.
http://en.wikipedia.org/wiki/History_of_the_Internet
Yes, it is actually fairly accurate and is kept under close scrutiny by the myriad of people who watch over that portal.
For a more terse, though somewhat euro-centric branded, view of the growth of the Internet, there is a good web movie online at YouTube that does quite well. See below.
Hope this little informational walk-through helps you understand a little bit more about the technology we now use everyday.
Kim Gentes