IBM and ATT had major labs and were vitally interested in computers talking to one another as early as the late 1950s and early 1960s. Bell Labs invented UNIX in 1969; it made the internet possible. IBM invented FORTRAN and hard drives in 1956. Bell transmitted packet data over lines in 1958. Texas Instruments invented integrated circuits in 1958. In 1961 Leonard Kleinrock published a paper on packet switching networks. Bell Labs made the first modem in 1961. Digital Equipment Corporation produced the first minicomputer in 1964. In 1965 time sharing at MIT and mail command started. Intel began in 1968. The year 1966 saw the first use of fiber optics to carry telephone signals.
Yes, the RAND corporation came up with a design for a decentralized network that could continue to communicate in case of a nuclear attack. However, they did not invent all of the technology that makes the internet possible.