What is a good thesis statement for this topic? Throughout the novel, we learn that Gatsby’s goal in life since he was a young man is to win...

You could argue that Fitzgerald denies Gatsby his dream just as it seems as though it is about to come true in order to make a point about the impossibility of the American Dream.  Tom Buchanan has old money, money that he has inherited from his wealthy family, money for which he has never had to work.  Gatsby was not born into such a family; instead, if he wanted to provide Daisy with the kind of life to which she has been accustomed, he would have to earn his money another way.  Unable to find any honest way to quickly acquire the funds he needed (even an inheritance that was left to him was stolen away from him), he resorted to bootlegging, profiting from the illegal production, distribution, and sale of alcohol during Prohibition.  He longs to achieve the same status as someone like Tom Buchanan, and he seems to believe that money is all that is required to get there.  However, he doesn't realize that new money, money that has been earned, is of much less value to the upper classes than old money.  Further, the fact that Gatsby has had to resort to illegal means to earn that money corrupts the dream all the more.  When Daisy learns that Gatsby has made his money illegally, it is enough to push her back into her husband's legally rich arms.

George Wilson, husband of Myrtle, the woman having an affair with Tom, has also attempted to reach the American Dream, but legally, and he's been unsuccessful as well.  He lives in the valley of ashes with his cheating wife, trying to turn a profit but lacking in opportunity and being misled again and again by Tom.  In the end, Wilson kills himself and Gatsby, believing that Gatsby had been sleeping with Myrtle, who was killed in an accident by Daisy, and so everyone who'd been attempting to achieve the American Dream is gone.  Who remains?  Daisy and Tom: the selfish, racist, elitist couple who basically barrel over everyone in their path.  They have all the power and can essentially do whatever they want, and they survive.  If society didn't privilege people like this, then such an outcome would not have been possible.  If society truly valued loyalty and hard work, then Gatsby and Wilson would have lived prosperously.  The fact that these two men, the ones who were most cheated of the dream, die shows that the American Dream is really only a corruption of an ideal at best.