In The Great Gatsby, one of the main themes is the "American Dream." People in the 1920s determined one's success by having self-made wealth and happiness despite one's classification in life. This success was shown through the materialistic things they owned such as their cars, houses, clothing, etc. as well as their social life. Fitzgerald illustrates this through the setting of East Egg. Here, the reader finds Daisy and Tom Buchanan whose lifestyle is the impetus for the destruction of the American Dream because there are no values or morals for those seeking the American Dream in the East Egg. In contrast, the West Egg where Nick and Gatsby live represents the American Dream containing a moral existence and basic values. These two "worlds" are in constant conflict throughout the novel. Both desiring the same dream, but with a very different means and outcome.
Lastly, the Valley of Ashes represents the totally destruction of the "American Dream," where money is valued above all else including morals such as God and religion. Thus, the total corruption of the American Dream is symbolically seen in the valley as a pile ashes, watched over by the eyes of Dr. Eckleburg.
Yes, you're right; the Valley of Ashes is indeed the place where the dream has died. The fact that everything is covered in ashes and is closed down, except for the gas station, is extremely symbolic.
West Egg represents those who have worked their way into the status of being "new money", through legitimate (like Nick Carroway) or illegitimate (like Gatsby) means. East Egg, however, represents the "old money", where residents such as Tom and Daisy have inherited their money from generations past, and have full possession of the American dream, often at the expense of others below them.
This book has a wealth of symbolism through out. The concept of East Egg and West Egg are literary representatioins of old and new money. East Egg referring to old money and West Egg referring to new money. This can be thought of in a broader sense as the world that is ever expanding seems to have roots and foundations in the east (hence the correlation of old money), and is growing toward a newer and prosperous west (the correlation to new money). While the story is staged in the East, it really is about it's path toward the west, and the movement from old money to new money. There is a great deal of cynicism in the older, more traditional thought with regard to money, where the newer more modest ideas and wealth seem to come from the north and the west.
You asked if the valley of ashes is where the American Dream ends and to this I would have to say I think, no. I would say the valley of ashes represents the waste products of what wealth has created when people living in opulence indulge themselves, what is left can often be devistating. But, also consider, maneur is the waste product of animals, and it is the very thing that fertalizes growth for the next round of life. So, the valley of ashes represents a burning of old soil, and represents a new begining for what is next to come.