Currently experiencing same issue I have yet to find a fix or anything vaguely similar on the internet.
Symptoms:
-Launcher seems sluggish
-Idling it begins scanning for patches but after about 3 seconds deems its up to date
-Clicking launch plays the sound but nothing else
-After idling for a decent amount of time the eula will appear twice as usual after a patch
-Game will still fail to launch after that
Have tried:
-Launching in admin
-Cleaning registry
-Excluding in antivirus and firewall
-Reinstalling
-Deleting certain folders pertaining to the launcher
System is:
Windows 10 x64bit - possible win10 issue?
SLI 770 - Had SLI issues in past
Just wondering if OP uses bitdefender as an antivirus as well because it's been causing me a lot of issues with LOL as well.