From what I found, in 1957 the Soviet Union launched Sputnik 1, the first satellite. Beating the United States into space caused concerns for the US military. Afraid they could launch bombs into space and drop them anywhere on earth lead to the creation of the Defense Advanced Research Projects Agency (DARPA).
Within 18 months DARPA had created the first US satellite. They appointed Joseph Licklider to head the new Information Processing Techniques Office (OPTO). He had a vision of a countrywide communications network and hired Lawrence Roberts who head the ARPANet network. In October of 1969 communication between the University of California and the Stanford Research Institute was reached. From there, here we are.
Military communication played a large part in the creation of the internet.
It is hard to determine who played the most important role in the creation or expansion of the internet. Different sources point to diffrent people or organizations but I believe the Military was definitely our starting point.
http://wiki.answers.com/Q/When_was_the_Internet_invented
http://en.wikipedia.org/wiki/History_of_the_Internet
www.isoc.org/internet/history