My client is not loading me in

Due to an issue that started happening about 3 months ago i cant load into the champion screen after the champion select counts down. My screen goes completely black and i only see my mouse icon, shorty after a 'ding' sounds can be heard and an error message saying "Unable to connect to the server. Please check your network connection and attempt to reconnect to your game" appears and now i have just got new internet hooked up in my house today becaus i moved and this issue happened at my old house on a friends internet. I have barley played since other then possible once a month on someone elses computer because mine cant seem to load in. Im extremely annoied and have been banned for this because im comstantly getting "leaver buster" back to back while trying to fix this, ive made several accounts to try to login with so my main dosnt get banned to unplayable. Ive sat in 20+ minute que because of A leaver buster que ban just to get mad trying to load into another game. Please respond with help.