Recommend me a desktop
While I don't have much money right now, the desktop computer I have right now is garbage. I would like a desktop computer that could:
*Run Dolphin games at full speed
*(Optional) Run SuperTuxKart at max settings (i don't mean 0.8.1, i mean current git, which has higher requirements for max settings)
*Run Ioquake3 based games (Open Arena) at max settings (r_flares and all that)
*Have as few non-free blobs as possible
*Have Windows drivers for every component (I don't like Windows, but I am not the only person living at my house...)
*Be as cheap as possible.
*Intel cpu is required, but I don't care much about what gpu is used, as long as it works and has decent linux open source drivers. (minimum graphics card requirements DirectX11.1 and OpenGL 4.4)
The laptop I am typing this on can't run dolphin games at full speed and requires nonfree firmware (*cough*Radeon*cough*).
You can buy any desktop computer with an Intel graphical chipset (perfectly driven by Linux-libre). Given your requirements, I believe you want at least 4 GB of RAM.
If you seek a free BIOS, your search suddenly becomes much tougher (and the price higher by lack of choice).
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By "Dolphin games", I assume you mean GameCube? GameCube emulation requires a lot of power (since emulation is necessarily a lot more expensive than using the original hardware), though I don't know how much, so you won't be able to slack on it. My brother has some kind of slightly old gaming laptop he got refurbished, with an Intel Core i7 CPU and some sort of Nvidia card; it wasn't enough to run GameCube games at full speed (he was playing Super Smash Bros Melee).
For the GPU, just use Intel integrated graphics. All modern Intel CPUs come with one. If you find you need something better, you can get an Nvidia card later (doing your research to make sure it works today if you need it to work with Linux).
If you need wireless, you will need to watch out for that and try to get one with an Atheros card supported by Linux-libre. Otherwise, you can just use ethernet; that usually works without blobs (ethernet will probably be fine for a desktop PC).
For your DE, Elementary from https://launchpad.net/~elementary-os/+archive/stable is pretty good.