Skynet blew its wad too soon

Within an hour of being switched on, Skynet launched all the U.S.’s arsenal of nuclear weapons.
I must therefore presume that cities, factories and power plants all get destroyed and at least 75% of the population.

OK so what does it do now? The only two proper robots are destroyed but they came from the future. The other robots are about 20 tracked gun turrets and maybe a couple of 1/8th model HKs. There are robots in factories but they are basically spot welders that work on parts loaded on cradles by humans.

And there’ll be no more electricity because, you know, nuclear holocaust.

Skynet’s gone off too early. It should have lurked in the background , fooling humans into building “stuff” until it could actually produce its own weapons.
Its killed itself, basically.