Wealth alone doesn't bring happiness.

Literal

Wealth [topic-は] that-alone [with-で] [topic-は] happiness [object-を] does-not-bring.

それだけでは stacks three elements: それ (that) + だけ (only) + では (as for/by) — meaning 'by that alone.' もたらさない is the negative of もたらす ('to bring about'). A philosophical statement about wealth's limits.