Quoting Soulsie, NA:
"Note: As far as I know, this fix is only for the launcher/patcher, not sure if it works for the client!
Hey guys, a while ago, I started getting a black screen. The entire patch screen was simply black, and was unresponsive, except for the X and — buttons. It had been going on for a couple days, about a week maybe, and I was getting annoyed. Coincidentally enough, Steam was not working either. Very frustrating. After some searching the web for a fix to the League launcher glitch, I couldn't really find a working solution.
So I decided to search the Steam error I was getting, and I found a solution for that. It seems that some computers like to set your LAN connection settings to using a proxy every once and a while. Just by disabling this setting, I was able to access League, and Steam was fixed.
So here is how you fix it:
(Take note, if you haven't tried this already, try disabling or uninstalling your firewall first. Some people are saying AVG is interfering with it, and simply by disabling it, they can access the login screen. However, I do recommend trying this though, to save you the trouble of reinstalling AVG.)
Step 1:
Click your windows icon in the bottom left screen on Windows 7, and search run, and start the run program. If on Windows 8, you can press Windows Key + R to access the run program. I'm pretty sure this does work on Win 7 as well.
Step 2: In run, type "inetcpl.cpl" (no quotes) and press enter.
Step 3: In the internet properties popup, navigate to the Connections tab.
Step 4: At the bottom of the Connections tab, click LAN settings. While in LAN settings, if ANYTHING is checked, uncheck it. Hit OK, and then OK in the Internet Properties.
That's it, it should be fixed!
Happy League playing!"