It would be stretching it to say either of them came out of a counter-cultural movement. The Internet certainly didn't come out of the counterculture - when I first got on it in the 80s it was run by the Department of Defense's Defense Advanced Research Projects Agency, and most people called it ARPAnet using those initials. It was created and run by military contractors and was not countercultural at all.
As far as the PC, there's a little more of a case but not much. There's a long chain of events needed for the PC to exist, from Bell Labs inventing the transistor in 1947 to Intel releasing the Intel 8080 in 1974 that has nothing to do with the counterculture. Ed Roberts and Forest Mims meeting at Kirtland Air Force Base where they decided to form MITS, which would go on to sell the Altair, is not too granola-y either.
The idea that the counterculture spawned the PC and the Internet is ludicrous. As I said before, there is no real story of computer gurus who are left-wing, the story is more the few leftists who are computer gurus. There has been a ton of hype about how computers are empowering, how it was spawned by entrepreneurs in their garages and so forth, and a lot of people swallow the hype. They were the creation of either decades of government R&D (the Internet), or a government-granted monopoly to a massive corporation, or both government money and a monopoly (the PC). That a few left-wing hippies made some money out of it is a sideshow. And the real story of the left-wing hippies, or even apolitical techies who did not have the hard-nosed evil businessman mentality, is that they usually got screwed out of their inventions.