BSODs caused by ntoskrnl.exe and win32kbase.sys while playing League

It's easier to copy/paste the chkdsk log into a txt file, or export it from the eventviewer, and upload that :)

In event viewer, a search for chkdsk and/or wininit should help find the right logs.

Run chkdsk again and follow the instructions provided in my post, chkdsk in read mode isn't very useful

I see the issue, the uploaded log is from 5 days ago.

Code:

Log Name:      Application
Source:        Chkdsk
Date:          04/05/2017 17:03:58
Event ID:      26226
Task Category: None
Level:         Information
Keywords:      Classic
User:          N/A
Computer:      DanielPC
Description:
Chkdsk was executed in scan mode on a volume snapshot.  

Checking file system on D:
Volume label is HardeSchijfD.

Chkdsk was executed in read mode

Code:

Log Name:      Application
Source:        Chkdsk
Date:          10/05/2017 16:44:40
Event ID:      26226
Task Category: None
Level:         Information
Keywords:      Classic
User:          N/A
Computer:      DanielPC
Description:
Chkdsk was executed in scan mode on a volume snapshot.  

Checking file system on C:
Volume label is NieuwVolume.

What error code was provided by sfc?

No problem, but I do want to ask you to read carefully for next times, it saves us both a lot :)

Now, please run following command in admin command prompt

Code:

chkdsk C: /r

I'm not sure if you've overlooked this part, so I'm quoting it here.

Note
Run the tests on all hard drives/partitions!