League Will not work

WEll, i've had the game for a while and i have become very fond of it to the point where i've bought skins for some characters but it wont work anymore. I've tried many troubleshooting tips but none of them have worked. I've repaired, reinstalled and done other things as well as update my computer. By the way, i have a Mac book pro that i purchased in 2012. It's nice it works but im not sure what the problem is, if its my computer or if tis the servers or the programs. The problem is that after the champion select the screen goes blank and i have to force quit in order to get back to the LOLclient and try to reconnect but nothing works. Now i have a 20 minute ban. I've never left a game on my own its always been something to do with the game. I really like the game but if someone could help that would be great, otherwise i will consider uninstalling the game permanently. Thank you for any help or input