Define happiness. If you're looking to become happy through self-success with a career held for many years, then simply having money won't buy you that happiness. Unless you're willing to go to school for it and work your ass off. In which case, money will definitely help with that and could probably buy you happiness in the end. But most people with money don't actually try to make anything of themselves because you tend to do that in order to make money, which they already have.
But money can definitely provide happiness. And it can make you feel really good about yourself, if you know how to use that money. Donating part of your money to the less fortunate can be very fulfilling and rewarding, and if you believe in karma then you'd be gettin a boner. For me, I can think of plenty of things I would love to buy to make myself happier. And, since I'm currently in school, I'd probably buy things to give myself a better chance at a satisfying and rewarding career.
While money can't buy happiness, it can surely help provide happiness, be it short-term or long-term.