Terminator Question: How did Skynet rebuild and survive?

In terminator 2, Sarah and co. destroy the t1000, the leftover chip and arm (from the first movie) and arnold. They also DESTROY the entire cyberdine building and the only man who made any sort of breakthrough on creating skynet. Now, in T3, they shift the focus to General Brewster, but I really don't think that his tenacity and some interns' elbow grease recreated skynet. Can anyone tell me how in the hell Skynet was built after all this? and please don't cite the series' profitability because I've acknowledged that and i'd really like to think that James Cameron wouldn't sign off onto a paradoxical piece of crap, just for a few bucks. (Or at least I hope Mostow needed cameron's blessing to do it)