If your login screen does not look like this your friends list/in game chat will not work!!!!
The client login should look like this: https://imgur.com/a/oXAVy5W
As others have stated there seem to be "two" clients..... the old league client and the new Riot Client. People have said to delete the Riot Client folder in the C drive (or which ever drive letter you have the game installed) but if you are like me, I didn't have that folder. If re-installing the game didn't work for you either, here's what you do:
Go to C:\Users"yourwindowsaccountnamehere"\AppData\Roaming\League of Legends - you'll see the much talked about "Riot Client" folder there. Delete the whole folder. Then go to C drive or wherever game is installed and launch the league client, it will update the client to the new one.
please note, to see AppData info you'll need to click view and check the box to show hidden items