The parts list can be found in step 1 of the MAGPI instructable. I had acess to a 3D printer so it was no problem attempting to 3D print the parts. I was able to order everything from Adafruit that I needed as well, which arrived about a week later. The parts from Sparkfun (the Arduino Mini, the battery and the battery charger), however, were all sold out. To solve this I instead ordered the Arduino off amazon, where they luckily had three items left.
The place I bought the Arduino Pro Mini 3.3v can be found here: http://www.amazon.com/gp/product/B00JNYXC8Q/ref=ox...
The next problem required finding a new place to purchase the battery and charger. I searched just about everywhere and wound up reading a bunch of sites that seemed to be in German and Arabic, but those weren't really going to help, so I had to figure out something else. I went to Adafruit and searched for similar batteries that might be available and found that they did have in stock a similar battery, except it was 500 mAh instead of 400 mAh. This wasn't going to be a problem, though, so I went ahead and ordered it. The battery did end up being slightly too large, but I'll talk about that in just a little bit. Along with this, I also ordered the charger that went with it. This charger was slightly different as it was a USB connector instead of a micro-USB connector and did not have holes to connect to the positive and negative terminals of the battery. I'll talk about this later as well.
The battery: http://www.adafruit.com/products/1578
The charger: https://www.adafruit.com/products/1304
Now there was one last problematic issue for obtaining the parts and this involved the right angle male headers. I assumed we had some of them lying around (we did have absurd amounts of the straight ones), but, surprisingly, I found that we didn't have any right angle ones. To solve this I broke off a row of 6 then bent each one with a pair of needle-nose pliers, creating my own right angle male header.
After waiting the week to get the rest of my parts, I began constructing the MAGPI by attempting to 3D print the top, bottom and PCB.