The parts I have:
1. 3.9" x 5.7" motherboard w/ 300Mhz Geode fanless CPU
2. 128MB PC133 SO-DIMM
3. 9.0 GB 2.5" hard drive
4. 8 D battery clips
5. 12v AC adapter
6. a cardboard box
7. Two 7805 5v voltage regulators
8. Two sliding switches
9. Logitech dual analog gamepad
10. 2.5"-->3.5" IDE cable
11. 3.5"-->2.5" IDE adapter
The parts I need:
1. PSone LCD (soon to arrive)
2. Another 7805
Planned software loadout:
1. Windows 98SE
2. SNES, Genesis, NES, SMS emulators
3. JoyToKey
4. Alpha Centauri
5. SimCity 3000
6. SimCity 2000
7. Sonic CD
8. Master of Orion 2
9. Civilization (various versions)
Construction status:
My first attempt to start the tiny motherboard failed. Turns out that, while I had a molex power source connected and routed into my Desktop, that wire was not actually plugged into the power supply. Stupid me. After that, I got it working.
Then came the next problem: the motherboard would not recognize it's hard drive. I spent most of an hour changed the arrangement of the IDE cable: the motherboard connector had 44pins, four of which were for power, but the IDE connector had only 40- it excluded the power pins- and the documentation was shoddy at best. After fiddling with it, the chances of me messing it up severely increased, and low and behold, I set the 3.5"-->2.5" adapter on fire!
The damage done:

Only then did I realize why the hard drive wasn't working: the molex connector wasn't plugged in!!! That was the second time something was either unplugged, or plugged into the wrong port, but it wouldn't be the last.
Despite the burnt adapter, it still worked! I booted Windows 98SE into the drive without trouble. Somehow the hard drive avoided death during the small fire...
Here is the setup as seen next to my monstrous desktop, which was supplying the power. The ruler is there for reference:

I went on to load the first few emulators into the computer, but I haven't any screens of those running. Basically, this is how the PCp is performing at the moment:
Genesis: (Kgen98) full speed
SNES: (Zsnes) MarioKart: practically unplayable/ scrollers: laggy/ RPG's: acceptable performance
NES: (Nesticle) Giving me a heck of a lot of trouble; the games barely run
Sonic CD: acceptable performance
Needless to say, do NOT use Geode CPU's, they simply don't have the oomph of a P3 or P2 counterpart. If you want to save power, go for a 667Mhz Eden CPU, or the more power-hungry Via C3's.
Here's just some other random pic:

I'm currently working on the power circuit that will allow the PCp to run off either batteries or an AC adapter. Both of those are 12v sources. Some of the current is dropped to 5v as well for the motherboard and hard drive via an array of parallel 7805's (to allow for greater AMP ratings). I will post a crude but effective image of the planned curcuit momentarily.
EDIT:
The power circuit:





