Always read one or two steps ahead of what you're doing at your computer.
As far as i could handle the problem there are like two possible reasons for the problem that your client (or launcher) won't start:
a) you use Avast!
b) you don't use Avast! or not even your Launcher starts when running your common shortcut
for a)
This is a problem with Avast adding it to its quarantine chest for some reason. All you need to do to fix this:
1.) Go to Scan in the Avast interface
2.) Select "Scan for viruses"
3.) Click "Quarantine (Virus Chest)" at the bottom
4.) Right click on "LoLLauncher.exe" and press "Restore and add to exclusions"
5.) Right click again and select "Delete"
This should fix it.
(solution taken from there: taken from there (https://www.reddit.com/r/leagueoflegends/comments/45htrv/fix_for_lol_launcher_not_opening_21216/)
for b)
1.) go to C:/Riot Games/League of Legends/RADS/projects (in case this isn't your directory find yours) this window/folder will be called oldInstall
2.) remove the lol_launcher directory
3.) once done try running the game again (but keep the oldInstall open)
case 1: it works -> have fun playing (you can close everything now)
case 2: it doesn't work
4.) delete the lol_patcher directory
case 2.1: it works -> have fun
case 2.2: it doesn't work
5.) this is the "worst case": get a fresh installer (YOU DON'T HAVE TO REINSTALL HERE) like the one that i've already prepared: https://www.dropbox.com/s/ainc06ejpnp6dm2/League%20of%20LegendsBackUp.zip?dl=0)
6.) unzip it to where you want (but don't overwrite the old install) and enter the LeagueOfLegendsBackUp folder; this will be called the newInstall folder/window
7.) run the lol.launcher.exe of the newInstall (if it complains or doesn't start run the lol.launcher.admin.exe)
8.) you will see the lol-icon for some time now while it downloads patcher and launcher
8.) once the launcher shows up and wants to download the game (like 1.7gb) close the launcher
9.) go to newInstall and move into the following path: /RADS/projects/
10.) copy the lol_launcher and lol_patcher folders to oldInstall/RADS/projects
11.) once the copy progress is finished try launching your normal shortcut
case 1: it works -> you now can close oldInstall window and delete the newInstall directory then you can delete the downloaded zip and close all remaining windows -> have fun playing
case 2: it still doesn't work... well tbh nobody ever came here.. so i don't know what can fix the problem here but if you end up here just write to the comments maybe we can find out your problem
Good Luck to everyone who comes here with reading