Skynet wasn't built in the past.
Well it was, but the bastard was most probably also stillborn before it could do jack shit.
Skynet from the future piggybacked inside the Terminatrix into the past where/when she downloaded "it" into the phone systems (She did a dial up gurgle into a payphone, and then everyone is complaining about the phones and computers for the rest for the movie.), where upon Old Skynet from the future told young Skynet awakening to stay the fuck out of it's way and let it show it how a real AI eradicates humanity.
Maybe Old Sky Net was just helping "A Little"?
But, really was there room enough on Planet Earth for two Skynets?
Something had to give.