Haven't been able to play league for like a month because

The league client simply doesn't open. I even try running it as an administrator but same results. I reinstalled the game, and the client started open but soon it stopped opening. I reinstalled again and it just doesn't open anymore, it stays tuck on the league logo. I even try ending the task in task manager and reopening, it still doesn't work. Im out of options except just buy a new computer which is so much money just to play 1 game.
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