If you can't connect to the loading screen try the above.
Servers are busy, lotta people tryin get in.** Keep spam reconnect and you good.**
If you got a black screen, try converting both resolutions to the same; there might be a display problem.
You can try making it windowed too from client options or ALT + enter.
Also, if that doesn't work.. make sure you aren't alt tabbing a lot when going from champ selec. to loading screen; that can cause it.
If you do get a black screen, a possible fix would be to end all LOL tasks from task manager and reconnect again. Don't watch youtube or Mia khalifa just let the **game load..