I am pretty surprised seeing people not knowing that Internet creation was state sponsored. Do you really imagine corporations spending millions of dollars on something that may never become profitable and even if it would, it would still take decades to do so? If we would let corporations sponsor our technological/science development, the technological/science development would stop.
Not stop, but it would be much more short sighted, on average.
It's highly likely that you're using stuff or derivatives thereof invented at Bell Labs to communicate in this thread, for instance.
IMO people often exaggerate the importance of the government in the creation the internet, usually for political purposes.
The original work on the internet was state sponsored because only the state had an application for the internet - communication systems that are robust to a nuclear attack. The internet was planned to be a part of nuclear command and control and this didn't have an obvious civil application.
Once there was a civil application for the internet (originally email) - huge amounts of funding was provided by the private sector. Think about all the prerequisite technology required for an early 90s westerner to get access to email(/BBS): dial up internet modems, internet service providers, email servers, personal computers, graphical interfaces driven by keyboard and mouse, ethernet framing protocols, mass production of hard drives, unix for the ISPs to run, etc. For the most part, these are all privately funded things.
If civil society had had a pressing application for the internet in the 1960s then the internet would have been invented by the private sector and that can be said with some confidence because the private sector invented nearly everything else in the ecosystem of required technologies to actually use the internet.
There's probably also a political selection going on when people choose the internet as "the" key foundational technology. Why not the personal computer, the C programming language or any of the things listed above. They're all arguably as important. Note that in Fallout lore, the main reason there is no internet is because there is no transistor (though maybe an internet based on vaccuum tube computers is technically possible - telephones certainly used vacuum tubes). The transistor was of course an invention of the private sector.
Anyway, back onto topic: I thought more about the reason why the internet is not present in fallout. I think mass communications, whether telephones, a post office or the internet make it impossible to sustain any kind of post-apocalyptic world. While communications don't in themselves provide any solutions to core problems of post-apocalyptic societies like access to water or irradiation they allow for whatever advances have been developed to spread rapidly. One of the main underlying features of a post-apoc society is that society is broken up and disparate. The internet would remove that feature fairly quickly and so while the official reason there's no internet in Fallout is "no transistor" I suspect that really the writers went back in time removing key technologies until mass communication systems were impossible.