Earlier quoted context omitted.
If you built it from real hardware, you'd be going to the store to buy a couple thousand NAND chips, like this: http://www.digikey.com/product-detail/en/SN7400N/296-14641-5... And a giant honking breadboard.
It might be beyond the scope of a normal hobbyist project, but writing Verilog or VHDL to drive an FPGA might bring interested people half of the way there. You mentioned Altera design software in another post; I don't know if Xilinx's is any better (I'm guessing not really), but Digilent sells FPGA boards intended for the educational market at a pretty reasonable cost. Powerful enough, I'd reckon, to allow for somet…
Doing it on an FPGA, without extensive handholding and in real-world languages, would be about a year of work in my estimate. This is assuming you build your own CPU (in procedural VHDL, not at a gate level) to implement an existing instruction set, and use the manufacturer's provided memory blocks, video blocks, etc. For reference, an experienced FPGA programmer would take about 2-4 months full-time to emulate something like an NES.
It would be a really good experience, and it's the kind of thing a comp. eng. degree prepares you for (we do a capstone project at my school which is like this). As a bonus, you'll also cover analog electronics (which are infuriating) and as much comp sci. and math as you're willing to take on.