In the Terminator storyline, Skynet was originally installed by the military to control the national arsenal on August 4, 1997. On August 29 it gained self-awareness[1], and the panicking operators, realizing the extent of its abilities, tried to pull the plug. Skynet perceived the attempt to deactivate it as an attack and came to the conclusion that all of humanity would attempt to destroy it. To defend itself, it determined that humanity should be exterminated.
Upon its creation, Skynet began to learn at a geometric rate. The system originally went online on August 4th 1997. Human decisions were removed from strategic defense. It originally became self-aware at 2:14 am Eastern Time on August 29th, 1997. In the ensuing panic and attempts to shut Skynet down, Skynet retaliated by firing American nuclear missiles at their target sites in Russia. Russia returned fire and three billion human lives ended in the nuclear holocaust. This was what has come to be known as “Judgment Day”. Terminator 2: Judgment Day
Old series had it in 1997, don’t know anything about the new ones.