So, What's the Problem?
Who or what is building all those Schwarzeneggers?
At the time when Skynet initially nukes the world, it's still just a computer program drifting around the Internet. Sure, it has access to nuclear launch codes, but not to more delicate equipment like opposable thumbs. Even if we assume that, in the world of the film, Skynet is able to hack into and usurp control of every factory and power plant through the Internet, it's still inheriting a world of machines designed to be operated by humans. That means valves need to be turned, buttons need to be pressed and levers need to be pulled. And just in case you're assuming that Terminator takes place in some kind of post-valve world, these scenes from Terminator Salvation would seem to suggest otherwise:
"Wait, I'm not here to kill you. I just need you to show me how these valves work."
"We've got to get away from these valves. If they find us, they'll make us turn them."
If you're thinking that Skynet probably just employs a division of Terminators to operate its factories, you're missing the point -- the computer didn't have access to Terminators back when it killed off all the humans. In fact, the most sophisticated robot that Skynet had access to at the time, the T-1, was a goofy-looking tank with Gatling guns instead of hands that could barely fit through a doorway, let alone turn a valve.
It can play the guitar surprisingly well, though.