Self assigned IP address I've done a clean install of OS X El Capitan recently, and everything worked fine. 

But as I came home, I couldn't connect to Wi-Fi. It states that it has a self-assigned IP address and will not connect to the Internet. 

I've been on many forums, and found no solution. Wi-Fi normally worked before the clean install and it still works on my side system, Kali Linux, which I'm writing from right now. 

I've tried to get OS X forget the Wi-Fi and then input the password again, but nothing changed. I've tried to enter a valid IP that I know it's working (I got to it through an app which remembered my computer on the Wi-Fi back when it worked), but still no Internet for me. 

The Wi-Fi has WEP encryption and I'm not able to access the router to change any settings, because the owner (which is not me) refuses to let me do some adjustments.
A self assigned IP address suggests that your system did not receive an IP address from a DHCP or similar protocol.  As Otto Andy Heiskanen mentions, restarting the DHCP server (by rebooting the router) can solve this issue often.  However you mention your Linux environment does get an IP address, which could point at a different cause.  You also mention that you are not allowed to access the router's settings: are you able to physically access it to pull the power plug?

If you can't access it physically, I recommend you compare the settings in the Linux environment with the settings in OS X.  Is the Linux environment getting an assigned IP address, or is it a fixed IP address?  Perhaps your linux environment is using a MAC address that is different from your physical MAC address?  Maybe there is some newly configured MAC address filtering enabled on the router?