"Genetic algorithms" was the first thing I could think of, since they take time on classical computers and can often produce results that human designers aren't expecting. Furthermore, they don't require any significant storage space, since they don't need to remember anything about previous generations, so your 16 GB limit is not particularly restrictive.

As a summary, and skip the next three paragraphs if you already know how a GA works: they mimic biological evolution by randomly recombining the "genome" of anything you want to optimize, such as a telephone network, chip design, road-map for a proposed highway system, and so-on. You begin with two randomly generated "parents" and, on each loop, recombine randomly chosen "genes" from each parent to produce five offspring. What you then need is some kind of scoring algorithm, which could be a simple formula or an entire simulation (estimated traffic of an airline network for a year, for example), which can calculate a score for each offspring. You pick the two best scoring children and pass them on to the next generation. Lather, rinse, repeat.

You can vary this by tracking multiple "strains" and allowing them to cross-breed, and you can add the element of mutation by randomly changing one of the genes every X-many generations.

Genetic Algorithms have been used to optimize modern telephone networks (cost, capacity, damage resilience), power efficient chips (I understand GAs are being used to optimize the ARM architecture these days), and one interesting case was the first known application: circuits that can distinguish between two musical notes. The result from a few thousand generations was a circuit--programmed on a FPGA--that had a totally unconnected sub-circuit. According to electrical theory, this sub-circuit could not serve any function, but on the physical FPGA chip was acting like a kind of resonance chamber, like the hole in a guitar, inducting a small current that in turn influenced the rest of the circuit. Such an invention was completely unexpected by the programmer, who had no idea such a circuit was even possible.

You run a GA as long as you have the budget or patience for. Sometimes you get excellent results after a weekend, but the longer you run it the closer it asymptotically reaches the ideal implied by your scoring algorithm. You might stop it once it looks like you've found the "ceiling" in the scoring criteria itself.

So I'd bring any reasonable OS and a program that runs a Genetic Algorithm that would essentially do the equivalent of asking a Genie for "infinite wishes": a design for a computer that would also have infinite processing speed, or at least the best possible. Might also run a GA to get the best performance-per-watt design for mobile computers.

Some other ideas, perhaps loaded up to run in series, although they would theoretically all complete the instant I hit "Enter":

A molecule with the lowest mass, highest strength (sheer and tensile), highest melting point and lowest cost that the best simulation of physical materials (my scoring algorithm) can judge. I'll come out and start a Space Elevator company.

A language translation matrix that can satisfy the largest and most varied collection of human-authored and curated "Rosetta Stones" that I can fit on any media I can bring into the room, both text and spoken, including dialects, slang, and inflection. Might solve world peace if we knew what each other was really saying.

Solve every conceivable "Traveling Salesman" route for every mail carrier and delivery company that I can sign-up in my 14-day prelude. Ka-ching. This might actually be the one that takes the longest to run, because I'll be filling up a lot of conventional Flash/portable hard drives with the results.

Find the safest, cheapest and densest way to store hydrogen that my physics simulator can judge, then sell the answer to automobile and fuel-cell makers.

Same for "supercapacitors" and sell it to electric car makers.

Solve Chess.

The potential of GAs starts to become a bit "magic wand-y" after you think about them for a while. Their limitation, assuming an infinitely fast computer, is really the scoring algorithm, and their limitation is human imagination itself.