I posted this on a couple of similar posts:
If you want, there is still a way to open the old client.
For that, what you'll have to do is: go to the Riot Games folder > then you delete the Riot Games folder inside it.
Once you open the regular client (hope you still have it somewhere on your desktop), you'll open the old client again.
One thing to remember is that every time the client updates itself, you'll have to keep deleting the folder and doing the same process over again.
It has worked for me with a couple of problems I've been getting with the new client, and also helping some friends that I told to do the same thing.
I'm still doing this for now until all problems with the new client are fixed. They should be solving most issues soon when you can no longer open the old client.