Public Expense & Private Profit
For computers, the period from development to commercially viable sales was about 30 years (depending on how you count). For the internet, it was also about 30 years within the state system before it was handed over, by a process that remains obscure, to private corporations.
And it's not a matter of public companies going private. IBM was a private corporation when it was making use of the government-funded MIT and Harvard computers, in government-funded labs (or fully government labs), to learn how to move from punched cards to electronic computers, and by the time it was going off on its own in the 60s, most of its production was for government agencies. Public support takes many different forms: funding, grants, government labs, procurement, etc. There are plenty of details in print. I reviewed some of Alan Greenspan's fantasies on this in a chapter of "Rogue States," dealing with the interesting history of transistors, technically "private" but in fact developed at public expense -- the only illustration he gave of the "entrepreneurial initiative" and "consumer choice" that drives the economy; the others were textbook cases of R&D within the public sector.
Typically, small companies were set up by faculty and researchers at labs, and if they were successful, bought up by private corporations, some later turning into huge conglomerates. Funding is a complex matter, and government procurement is also a major factor in keeping the companies viable. Also, there is just plain spin-off. Thus much of the avionics, advanced metallurgy, etc., that goes into a commercial airplane is taken over from Air Force development. And the links are so tight in other areas that it's hard to dissociate. Take contemporary trade by sea, based on containers, developed at public expense by the Navy. And on and on, wherever you look. I've cited many examples and sources if you want to research it further. It's mostly in history of technology work, and goes back a long time. Thus the US mass production industry, which amazed the world in the 19th century, was based largely on R&D within government armories. Same with roots of the automotive industry and much else.
There have been some careful studies of this by excellent economists, particularly Dean Baker, of CEPR (Center for Economic Policy Research). His basic conclusion is that if public funding of R&D for pharmaceuticals rose to 100% (it's now probably about 40%, depending on how you count), and the companies were forced on the market instead of being given extraordinary monopoly pricing power by the grossly mislabelled "free trade agreements" and (in the US) other huge public gifts, then savings to consumers would be colossal. According to big pharma records, about 40% of R&D is in-house, but that is highly misleading, because so much of it is oriented towards the marketing side -- copy-cat drugs, etc. And all the figures are misleading because they don't count the basic biology, almost all at public expense, on which it all rests. That aside, there are much more severe distortions introduced by market systems, inherently, to the limited extent that they function in these areas. Why are thousands of children dying every day in southern Africa from easily treatable diseases-- Rwanda-level killing every day, which could easily be stopped, not by military intervention but by bribing drug companies to produce drugs for them, instead of life-style drugs for the rich? Why are bacteria mutating much faster than development of new antibiotics to deal with them, leading to crises down the road even for the rich? One can't blame CEOs for that. They are legally required to produce for profit, not use, so the savagery, barbarism, and disastrous consequences are built into the system.