Today I was playing a ranked game as Katarina. My client crashed, so I entered the game a little late. I began laning vs Lux and got a single failed gank from my jungler. Level 6 comes around and I go to gank bot, which had been pushed by the opposing Vayne. Both junglers were down there and all were at very low health. I got super excited and jumped in for a free triple kill... And I get a Skype call, minimizing League. I tab back in as quickly as I can to find that I died. I was very upset. I head back into lane and die to lux twice because she was 4 levels ahead of me and landed her Q when I was away from Shunpo-able minions. At this point, 0/3, I very nearly gave up. I pressed escape and just barely stopped myself from quitting. (I have never rage quitted before.) Then, we teamfight. I wait, then seize my opportunity, jump in, and get my first Ranked Pentakill! We push down 2 inhibitors and a few minutes later we win the game.

tl;dr: Even if you have a terrible time early, if you don't give up and play well, you can still win your team the game!