The problem is the new riot client, it is garbage.
Solution:
1: Navigate to your League of Legends install path
"C:"install path"\Riot Games"
2. There should be a second folder in the "Riot Games" path called "Riot Client"
3. Delete "Riot Client" folder
4. Go in to the "League of Legends" folder
5. Run league of legends from there
You should be able to boot into the old client without a problem and login and play
If you encounter the problem again, just repeat the same steps!
This worked for my non-admin school computer without a problem. I assume it should work for everyone
Share and like if it helped you!