We must be improperly using our cerebrum if happiness doesn't exist. It's an emotion, like anything else; it doesn't equal something, but has a profound effect on our personality and state of being.
Happiness is when your brain rewards you for an action by giving you a dose of endorphins, thus encouraging you to repeat that action. Any other forms of happiness are all in your head and with a stable enough mind, you can easily make yourself happy in most situations (or at least content), by simply relinquishing yourself of needs. Note here that there's a subtle difference between simple and easy.