I found the smallest normal PC motherboard I could find and wrote a custom BIOS for it...yeah bad me, reverse-engineering the original BIOS.
I used a PCI riser board to fit additional cards, and crafted two plastic rods with grooves cut into them to hold the cards in place, and attached the rods to the motherboard through holes that would normally be used to attach the board to a case. I then fitted the board monstrosity into a plastic shell that I had built at a plastics shop about an hour away. The rest was just basically cutting holes in the shell to attach the additional I/O ports and building risers into the shell to hold the DVD-ROM and HDD. To power the beastie, I found a very efficient, very small 450W power supply and attached an exhaust fan to the back next to it.
The whole process involved finding the smallest components possible that would get the job done to spec. It wasn't easy.
After I had abandoned all hope of mass-producing Leviathan, I attempted to design a handheld...that was even more difficult, because you really have to know computer design...nowhere near the same as building a normal console out of x86-compatible components. Since I was just starting out with "console from scratch" ideas, I based it on the familiar 65C02 and coupled it with a very basic graphics chip (I don't remember which chip I was going to use). For a screen, I found a very nicely done 320x240 pixel LCD screen available pretty cheaply. But after I had finished developing the schematic, I did a power profile and discovered that the machine would require way too much amperage. This was before Li-Ion batteries were widespread and built-in chargers were uncommon, so I had no idea how I would be able to power the damn thing...as it was, it would have required three 9V batteries to run it. So, I scrapped it.
Console design really isn't my thing though...I'd rather make games for existing consoles, like the PC Engine.