Game doesnt launch when clicking on "LAUNCH" Button on launcher

For the past few weeks, I'm having hard time to open LoL. When i open the launcher and I click "LAUNCH" on the top of the page to open the game, it closes the launcher and doesn't start the game. Even if you want 10mins or 30mins, nothing happens. But on my task manager, there is 3 tasks about LoL that are running ( Look @ Screenshots ). If i try to reopen the game, the logo is appearing, but nothing happens. ( Look @ screenshots )

So to be able to reopen the launcher, I have to open task manager, and close all LoL tasks.

After like 10-15 tries, then the game is launching... at last. Quite often it takes more than 30 tries to be able to play.

How to fix this problem?