That's the legacy client. I'd imagine you've fixed your problem by now, sorry about the late reply, I'm just a casual.
A fresh install of League should be using the new client. There are old files sometimes that linger that'll cause problems, like pando media booster and I had removed that manually before Riot release patches to remove it. If you have old legacy files, I'd recommend trying to copy your old config settings and then deleting everything with a fresh uninstall. Sometimes an installer won't recognize older files as a threat, but you'll notice because of the forced interaction causing crashes.
Go to:
Create a new file in my documents, name it Old Config.
C:\Riot Games\League of Legends\Config
Copy everything except Global and Champions into Old Config.
Delete C:\Riot Games
In the Windows search bar, type in "Uninstall a program" and pick the similarly named topic. Find League of Legends and uninstall it.
Do a complete fresh install of the 30-40GB file which is League of Legends. (It might honestly be less than 10GB)
Now, without looking at what your computer is doing, this only serves to make sure that there are no lingering files trying to interact that would've otherwised been removed and placed somewhere else. Other items to look out for are mods, which the new client isn't very friendly to. If you have League of Legends mods for the old client, find the that mod folder and delete it, although usually they're located within the C:\Riot Games folder (another reason that deleting this folder is necessary).
After troubleshooting the installation, the next area would be to discover what your computer is doing. Troubleshooting a computer can sometimes be easy, but I'm not a tech, so if need be you'll have to submit a support ticket to Riot with your logs so that they can analyze that.
https://support.riotgames.com/hc/en-us/requests/new