A) Money does NOT bring happiness. That is a proven fact.
B) Lack of money brings unhappiness. That is a proven fact.
You appear to be confusing A with B.
When you don't have enough money to get the necessities in life, then you are unhappy. When you get the necessities, you become more happy. Thus, initially, money brings happiness. But that trend ends quite soon. Once you have the necessities taken care of, then MORE money doesn't bring more happiness. You cross into category A.
The easiest examples are in the extremes. If you give a starving person money for food and shelter, he will be happy. His lack of money was removed, thus his happiness increased. But, if you give Bill Gates a million dollars, he won't be any more happy than before. Your money brought him no happiness at all.
The cutoff will vary from person to person, but often it is lower than most people think. Once your basic necessities are taken care of (food, shelter, etc), then you likely are in category A. If I gave you $5000 for a trip, you will be temporarilly happy. But once the trip is over, you'll be no more happy afterwards than before. Same goes with a bigger house, a nicer car, more electronics. Generally it is just a temporary feeling that doesn't last. The money ultimately didn't make you happier. Why? Because you just want something bigger and better than what you just got. The money didn't truely end your wants, it just changed the wants.
For example, suppose you wanted a 40" plamsa TV. Fine, but if give you money for it, you'll be no happier in 1 year then you are now. Why? Because in 1 year, you'll want a whole in-home theater and not just a measly 40" plasma TV. You still don't have your wants satisfied, so you still are no happier than you were to begin with. Suppose your parents buy a $100 million house today. You'll be no happier in 1 year than you were yesterday since you'll want that house to be YOURS and not your parents. The house did nothing but shift your wants.
Even if you did buy everything you ever wanted, you'll still have friends and family die, you'll still have aches and pains, etc. You'll still have to go through girlfriend/wife problems and arguments. Etc. Money never solves any of the true problems in life once your basic necessities are purchased.
Thus, most people in first world countries are in category A, where more money doesn't bring true lifelong happiness.