CPU, RAM, GPU: 1x single board computer
A Single Board Computer provides every component needed to build laptop, except for battery, display, keyboard and case, each of which can be added separately.
Single Board Computers provide CPU, RAM, GPU, motherboard and some other integrated features on a single board. They are full desktop computer system that is sufficiently small and low power consuming to be used as a mobile, DIY laptop. They are also very low cost (<$50).
The most important feature of Single Board Computers is that there are models that are fully open source. It is possible to build a fully functional laptop with Free Software only, including free firmware, wireless and 3D video acceleration drivers. It is even possible to get SBCs with open source hardware designs.
Single Board Computers with free 3D video acceleration (Etnaviv)
Nitrogen6X ($225): Quad core ARM A9 @ 1 Ghz, Freescale i.MX6, Vivante GC2000, 2 GB DDR3, best option, compatible with mainline kernels
Nitrogen6_MAX ($299): Quad core ARM A9 @ 1 Ghz, Freescale i.MX6, Vivante GC3000, 4 GB DDR3, faster Nitrogen6X
Wandboard QuadPLUS ($139): Quad core ARM A9 @ 1 Ghz, Freescale i.MX6, Vivante GC3000, 2 GB DDR3, cheaper version of Nitrogen6_MAX, not mainline
Open source hardware Single Board Computers
BeagleBone Black ($55): Single core ARM A8 @ 1 GHz, TI Sitara AM335x, PowerVR SGX530, 512 MB DDR3, fully open source except GPU, mainline compatible, https://github.com/beagleboard/beaglebone-black
OlinuXino LIME2 (€45): Dual core ARM A7 @ 1 GHz, Allwinner A20, Mali 400, 1 GB DDR3, mainline compatible, https://github.com/OLIMEX/OLINUXINO/tree/master/HARDWARE/A20-OLinuXino-LIME2
Radxa Rock Pro ($97.75): Quad core ARM A9 @ 1.6 Ghz, Rockchip RK3188, Mali-400, 2 GB DDR3, fast open source hardware SBC, mainline compatible, no gigabit LAN, https://github.com/radxa/oshw
Radxa Rock2 Square ($139.90): Quad core ARM A17 @ 1.8 Ghz, RK3288, 4 GB DDR3, 5V 3A, fastest open source hardware SBC, same SoC as Asus C201, https://github.com/radxa/oshw
Do not use Raspberry Pi, because it needs a proprietary bootloader to boot.
Low power consumption means low battery usage and low heat, allowing the use of USB powerbanks as the battery and a fanless design. All reference SBCs draw 5V 2A unless noted, which is the maximum provided by a USB powerbank.
Vivante GPUs have the open source 3D driver Etnaviv in mainline Linux 4.5+ that is fast enough for Quake 3.
-Can freely overclock CPU, RAM, GPU
-Easy to upgrade, just swap the Single Board Computer for a new one
-Easy OS installation, just write OS image to microSD card or USB flash drive
-Can use HDMI splitter to drive additional displays, but better and cheaper option would be to use a second SBC connected using TightVNC over gigabit LAN to drive a second display
-Can create beowulf cluster of SBCs connected over gigabit LAN and powered by USB to increase computational power and provide more ports