From "scratch," as in raw materials, absolutely not. Even the most dedicated home-fabrication hobbyists ( http://sam.zeloof.xyz/first-ic/ ) have come nowhere near achieving the transistor density required to construct the "OberonStation's" CPU or memory, whether taped out (laid into a chip design using actual silicon gates) or built using a programmable gate array.
From a circuit board etched by someone else and PCB components purchased online and soldered together by a hobbyist, certainly, without too much difficulty (the package used by the programmable gate array requires a bit of specialty equipment, but is within reach).
One other point about Oberon is that I _believe_ that because the design predates open-source FPGA toolchains, a closed toolchain is still required to convert the Verilog (high-level design describing the processor logic) into a netlist (FPGA configuration), and it hasn't been taped out into a chip, either. So, the book covers the design of a computer end-to-middle - that is, without covering how the block / HDL level design becomes logic gates, and without covering how said gates are then manufactured. This is probably fine - the scope has to end somewhere. The linked NAND-to-Tetris articles cover the other end - from logic gates up to typical computing constructs (adder, registers, shifters, etc.).
I suppose it depends on how you define "from scratch". Pretty much anyone can build a desktop PC from parts in a single day. That's what would make the most sense in this context as well, probably. Target a simple CPU design with a simple instruction set that you can understand.
If you want to go further from scratch... Designing a motherboard wouldn't be too hard, though it probably wouldn't be very good or reliable. Same with a power supply. Designing my own CPU is something I could probably do with several months' worth of effort, as a CompE. But actually making a physical chip of it is another matter entirely. It would be expensive and you'd have to pay a manufacturer to do it. Physically making your own CPU at home is pretty much out of the question, but you could use an FPGA. I have no idea how to go about making RAM or hard drives "from scratch". Same for monitors.
I decided I could fix my own cars when I “realized” that ‘if someone else can do it, I can do it’ as well. Turns out I had to learn a lot, but I learned it.
Fixing cars is of course learnable; we all know that mechanics exist. But computing hardware is usually built by really complicated machines. I honestly don't know whether it's possible for a person to make a CPU.
Click on Nana2Tetris in the link above. You'll find out a good bit about it. Modern CPUs are enormously complicated. Machines from earlier eras tend to only be of only middling complexity.
I think that Digilent FPGA board is discontinued so a bit more work to make it work on another board. You will have to modify the ucf file to match the pinout of another board. In particular you need a board with SRAM but a lot of newer boards have DDR memory.
