If we woke up tomorrow and...
cool-RR: I think it's a very interesting question.I would say three to five years. In my opinion, technological tools are overrated. Most things can be built by hand using common materials.Actually, it would be a very cool project! Take a bunch of hackers. Set up an isolated camp for them in a remote area. There will be no technology there, but there will be plenty of edible plants, fresh water, and some medical supplies. The hackers will be supplied with a sample of every raw material that Earth has to offer. And when I say raw, I mean, for example, iron ore. Have video cameras all around the place to make sure they are not bringing technology from anywhere. Measure how long it takes them to build, say a computer. I think it will be less than a year. (The reason I answered 3-5 years to the main question is because in the situation you described most humans will be busy fighting each other, and hackers will have less time to devote to rebuilding technology.)