If you are playing on a windows 10 machine, you don't need to restart your PC.
Here is a workaround if your loading screen freezes.
Step 1. Make sure Task Manager is not running at the moment. You can do this by hitting the windows button and closing it via right click, in case it is open right now.
Step 2. Make sure you are tabbed into the game.
What I mean by that is, when you try to tab out, Windows recognizes it, but League doesn't care. Make sure you hold alt after pressing tab and reassure that you are in the game client, perhaps even with a mouse click.
Step 3: Click the windows key on your keyboard.
Step 4. Press this button next to the search bar:
https://imgur.com/a/b1Iafwi
It's called "active apps" or "create new desktop", anything that allows you to "create a new desktop" is the right option (should be at the top of the screen after you click that button)
Step 5. Now that you clicked this button, windows will have redirected you to this desktop. Open the Task Manager here.
AND LET IT LOAD FOR A MOMENT(!)
Step 6. Kill the League of Legends process by either clicking it and pressing "Kill task" or something similar on the bottom right,
or rightclicking it and selecting whatever kills the task in the context menu that shows up.
IMPORTANT: DO NOT CLOSE THE LEAGUE CLIENT (Has the new league Logo, the circular one).
MAKE SURE YOU CLOSE THE GAME CLIENT (Square, old Logo).
Then Rito games should automatically redirect you to the client prompting you to reconnect.
If you notice immediately that your loading screen froze, getting back into the game, with an average PC will take you
30 secs to a minute instead of getting the remake thrown at you.