You may read thousands of posts about ELO hell, but that's just because of how huge the player base for league of legends is.
ELO does not exist. Yes, in the lower ELO's there will be feeders / leavers. But at the same time, the chances of the other team having someone like that are exactly equal to yours. So if you continue to play the ELO system does work and will balance itself out over time.
I think the first thing you need to do is step back and re-evaluate your play style, no offense meant. If you cannot bring yourself out of the 12-1300 ELO then it is quite possible that you yourself are not yet playing at a 15-1600 ELO level.
For instance, you have a feeder on your team, OK. The chances of them having a feeder also is very high, so prey on their weaker players, get some kills, remember to constantly CS and out farm them and continue on to carry your team.
No, I am not implying you can win every game in the manner, but as long as your wins are continually more than your losses your ELO will go up. Slowly, but it will increase.
Also, try duo queing. It makes it easier if you have a friend so you can play roles / hero match ups that compliment each other.