True Despair

I at least try and play a few matches a day to see if League will work for me. So far I lagged out so badly that I can't even use my computer. And when I finally got it working, it finally gave me a chance, the old Client window wouldn't close. Even now I still have it on my computer, it refuses to close, by the end of the match I had 3 League windows open, one went to the end screen when you win, another was still in the game with sound and animations, and the last one was the old in game window that lagged me out. It still hasn't gone away....... So I ask, should I give up? Or can this be fixed? I have no more money to spend but I wanna play league and am willing to try anything. This is the 2nd time this has happened. I wish I knew what was going wrong so I could fix it. I plan to uninstall then reinstall and see if that works.