A layperson named Steve McIntyre did just that, after reading the IPCC's 3rd Assessment Report and seeing the prominently featured "Hockey Stick" based on a paper by Mann et al., and wondering, hmm... perhaps this study is reproducible?
The rabbit hole that McIntyre and his colleagues have found themselves in over the last 10 years has, in my view, demonstrated the value of hacker-types taking an interest in climate science.
"Of crucial importance here: the data for the bottom panel of Figure 6 is from a folder called CENSORED on Mann’s FTP site. He did this very experiment himself and discovered that the PCs lose their hockeystick shape when the Graybill-Idso series are removed. In so doing he discovered that the hockey stick is not a global pattern, it is driven by a flawed group of US proxies that experts do not consider valid as climate indicators. But he did not disclose this fatal weakness of his results, and it only came to light because of Stephen McIntyre’s laborious efforts."
IIRC, despite the criticsim, the 'hockey stick' study and its author were proven right. Lots of criticism doesn't make it wrong, especially in politicized debates.
You should just stop with this line of thinking. You have to understand the scientific context and the limits of the data to learn anything. (Source: I know several contributors to the IPCC AR5 report, and I try to have the proper respect for their expertise.)
Great, so you're capable of writing highly parallel cluster-scale code in C that does intensive precision numerical analysis? Most choose vectorized FORTRAN or a combination of C++ and CUDA, but hey, knock yourself out.
CERN has a 3700 core supercomputer to crunch through this kind of data. You can rent that on Amazon for about $800 an hour, so I guess you're good to go.
Sorry to be so harsh here. While there's always desirable amount of "constructive naivety" necessary to try the impossible, you need to recognize that there's considerable amounts of expertise required to process and analyze data of this complexity at scale.
This is not like a movie where six minutes of furious typing can solve any problem.