I've had this problem myself.  Only once did I get an absolute full story.  Miserably I was as far from a pen and paper as possible and I actually didn't want to write the story.  I didn't like it.  Don't ask me how I got it.
However, one thing that did help for other half-baked imaginings, was drawing out the story.  Just quick sketches.  It gave me a bit of a story board.  After that things can be sorted out because it is on paper.  Try to make a mental movie in your head telling the story.  Visibly "see" the events occuring.
There is this also, sometimes our minds think some fantastical things, because that's exactly what they are.  Fantastical.  Your logical side may be telling you to give up your ridiculous notions subconsciously.  Which is why I suggested using the creative side by drawing, to reinforce the ridiculous.  There could also be an error in logic in your story which you can't imagine because you're not thinking with that part of your brain when you're creating the story.  Therefore, if you can even get the points down, ie. beginning, middle, end, then you can look at it objectively and see if it even makes sense.  If it doesn't initially, give it a little time, go back look at it again and find the gems.
Something I just thought of, you could be writing in the wrong style too.  You could be better at screen writing, short story/anthology, epic poetry, or who knows.  Experiment with a jack and jill story.  Something super basic.  Find out if you like one type over another.
You mentioned a lack of interest in writing earlier on or in school.  Please don't take this badly :|  It sounds like you weren't really interested in writing in school and I'm thinking maybe you didn't pay attention to the lessons that do help.  Things like plot skeletons and construction.  Try taking a writing class/course or go to the library and read those writing manuals.  It's amazing the stuff we take for granted, like skin.  Half the time we don't even make a note of its existance, yet without it - *ouch*!
Hopefully something I've written illuminates the dark recesses of your mind and boom! you'll be an author makin' money (a rare find).
Words and Time my life's Obsessions.