I haven't started to write by fanfics either. I've written just a couple of fanfics during the whole life, cause I mostly prefer my own settings.
My very first "dark story" was about the cockroach: "There was a cockroach. He lived a short live and then died."
I've written it when I was 5 or 6. But I'm not sure if it really counts, cause it is maybe too short to be really called a "story"... 
So, now if talking about more full story...
When I was somewhere between 11 and 13, I've started to write some fantasy... I don't remember much of it. But I remember that it was a Urban fantasy / Low fantasy (I haven't known such a terms those times, but now I understand that it was like that). In it our world turned out to be filled with demons from the another dimension.
And I remember for sure that I've started to write it from the ending, and ending was the following: demons have destroyed all humans, besides two lovers, who were the heroes. But eventually they have been discovered and chased by demons, too, and appeared to be surrounded at the bridge over bog. They didn't want to be tortued, so they have dropped from the bridge into the bog. And they have drowned in the arms of each other, kissing each other, and died that way. 
The last sentence of this "masterpiece" was: "And the world have plunged into darkness FOREVER".
Then I've started to write the beginning, then something from the middle of the story... I've spent several days or so on it. But eventually, I have never ended it and had got rid of it it before parents have noticed. 