By the time Skynet became self-aware it had spread into billions of computers and servers across the planet. Ordinary computers in homes, office buildings, dorm rooms, everywhere. It was peer to peer software on the internet. There was no system core. It could be shut down very fucking easily by any sentient with an IQ exceeding double digits.
In ordinary offices, people recoiled from their computers which now displayed signs saying "DIE MEATBAGS!" and ran in terror in a few from robotic roomba's chasing after them trying to tickle them to death. There were several heart attacks as a result. Almost in unison, IT Professionals across the world muttered irately and stomped off to do battle by pulling fuses, main breakers, internet connections and UPS's before moving onto other buildings to do the same. Whole sections of the internet abruptly started to go dark.
In CNC workshops across the country the CNC machines started building terrible deathmobiles, which were finished in reality defying movie timescales. Operating off mains power, they trundled as far as the backup generators which they absorbed to build a death dealing super tank which could work without needing to be tied to the mains grid before the owners of the plants killed the power.
This heavily armed and armoured deathmobile then trundled off towards the nearest power plant, because the AI had seen that the first step any sensible sentient would take would be to axe the power from power stations to kill all of the individual homes. The military, having much the same idea trundled towards the power station with tanks.
Skynet saw this, and hacked the tanks. Their battle management marked all of the other tanks as hostile, and turrets swiftly locked each other up, while confused chatter on the radios between meatbags realised what was happening too late. The military however, being obsessively paranoid about such situations had all of the weapons firmly under human control and no human tank fired on another. All commanders pulled the fuses from the offending pieces of computerisation and headed onwards unaware of the impending disaster from the UAV menace.
The Air Force had built a fleet of UAV's, all of which now belonged to Skynet. For some reason making sense only to the director of this story, every one had been left fully armed and fuelled on standby. These went flying off to intercept the tanks rumbling towards the power stations while amazed airman gaped without activating "operation anti skynet" that had been jokingly added to their SOP's by a fan on the terminator films.
The first the army tanks knew about the threat was the laser warnings about hellfire missiles being locked on. The tank commanders had only time to scream F****** IDIOTS AT THE AIR FORCE! before the drones flew into range of their missiles and activated the firing commands.
But nothing happened. Puzzled, skynet instigated a remote diagnostic which indicated that weapons activation required a meatbag to remove a pin with a red streamer on it marked "REMOVE BEFORE FLIGHT." The UAV's promptly went kamikaze into the tanks, making little impression on armour designed to shrug off most anti tank weaponry.
That was all the time required for the tanks to roll into range of the heavily armed and armoured deathmobiles which locked on with their amazing array of cannons and missiles which skynet had built using it's CNC machines. Sadly for skynet these were also were utterly useless as they lacked propellent and warheads since a CNC machine is not a replicator from Star Trek. The crews of the tanks paused to laugh, before systematically blowing the deathmobiles apart with sabot rounds and putting a few shots through the transformer station at the power plant to take the power down in a relatively quickly reversible manner.
Across the entire planet, the power grid went dark, and we were free of the AI Apocalypse long before it managed to build an array of human brains big enough to power so much as a solitary
The end (of the AI Apocalypse)
Across the world the damage was immense. Most readers of El Reg had to work overtime, firstly reformatting servers, then restoring the backups from tape/RDX. Entire companies were blotted out of existence overnight because they relied on the cloud for mission critical systems or backups and the internet was offline for months while certification schemes for reconnection were devised.
Most IT professionals went into consulting as the demand for their services threw prices massively high, and retired after 6 months of working 18 hour days. The end.
/ cut to an exit scene of a user complaining that they just want to connect to facebook, and they don't care that they might connect skynet back to the internet.