Luck (or RGN if you prefer) does influence your game, of course, but it's not the main reason that decide a win or a loss, or in your case, climbing out of low elo.
You are right about saying that there are trolls/afk/inters (and, bad news, it will always be like this in every elo you will ever be in) and those players does influence your game in bad way. But it doesn't happen every single game, and when it does happens it doesn't lead necessary to a defeat; you can still win despite having those players in your team.
In your case (i suppose from your last game) there is involved that Annie that apparently didn't play very well; and you assumed that she trolled (maybe he/she did, i wasn't in the game so i can't judge). But if you check his/her account, you can see that this player, most of the time, does have a bad KDA, even when he/she win. Now i know that you are thinking that is a "professional" troll/inter that get occasionaly carried, but he/she isn't. Why keep build items if she want to troll? He/she should just run it down in all of his/her game. If you look there are games where this Annie does have highest damage (so she is not trolling at least in this game) and STILL, a bad KDA. He/she is just a bad player that, i suppose, doesn't look enough at the minimap, doesn't have good positioning, and doesn't know how to trade. Also, she is a player that can't climb out of Bronze 3 (his highest rank apparently) even after 4 seasons.
Now, this kind of players, as i said, does influence your game and can make win it a bit harder, but even if you lose this game only because of a troll (even if i don't think so), what about all the other games where there was no troll, all your teammates where fine, and you still lose? Who to blame in this scenario? I bet you say something like "yeah enemy team was better". But this isn't the answer. Even if can happen that you may face a very stong team, and you can't win, the main reason that lead you to lost it's (wait for it...) YOU.
Just improve, man; work on your mistakes, become a better player, ignore those trolls, afk and whatever; if you are good you were climb no matter what. And if you want a proof, i was among those players who thought "ah climb out of bronze is impossible, bla bla bla" and i've been hardstuck in Bronze 5 for 2 years. But now, since i've become a better player, i can easily climb. And you can too. Just work on your mistakes.
http://euw.op.gg/summoner/userName=Elstir
