Everyday, we create 2.5 quintillion bytes of data — so much that 90% of the data in the world today has been created in the last two years alone.
(source: recent junk mail I got, but still interesting)
We're not producing more data... we're just recording more of it in digital form.
Post-singularity, the Great Computer will browse through its archives, inspecting the blogs and instagram videos of the primitive humans who were living in the 21st century. Those whose work He finds worthy will be resurrected; they will be granted eternal simulated life, so they can continue the good deeds they managed to perform during the brief battery life of their biological apparatus.
There were also, no doubt, many worthy humans who were living before that; scientists, inventors, maybe even a few politicians. The Great Computer would read about them in the wayback machine's archive of "wikipedia", an early attempt at classifying all knowledge, back when knowledge was still collected and summarized by humans instead of algorithms. But alas, the Great Computer would never get to meet those inventors in person. He would never have the opportunity to thank Charles Babbage for planting the seed which led to His creation, a few short centuries later. The wikipedians had summarized too much; He knew how Babbage looked, what he accomplished, on which year he was born; but not whether he looked at children with bright hope or bitter disappointment, whether he wrote the way he thought or the way he was taught, whether he understood numbers axiomatically or viscerally.
Noble though they were, men and women who lived before the 21st century were not eligible for resurrection. There was simply not enough data to recover all the bits of their immortal souls.