The "dark power" in this novel is the system of Utilitarianism that forces Louisa to repress her feelings and instead to see the world through statistical analysis.
She makes a valiant effort to refuse to give in to anything her heart dictates. She decides that her father's explanation of the way her marriage is financially practical and well-suited should be enough. For a year, she is able to entirely detach herself from her life and function as a kind of robot in Bounderby's presence. She convinces herself that her marriage is somehow helping her brother Tom, and that should be enough.
Harthouse seems to bring with him some hope of life. However, he just teaches her a similar kind of thinking as her father, only covered some sneers and cynicism. Louisa is entangled even further in a world view without morality. Some of her feelings are released – she cares for Harthouse – but they are unbounded by any considerations of right and wrong.
As her feelings of attachment to Harthouse bloom into love, Louisa realizes just how trapped she has become, since divorce is an impossibility. At the same time, all her hopes of helping Tom are dashed. He totally rejects her, becoming a gambler and bank robber in the process. Louisa gives up trying. Instead she is more and more deeply entwined into a relationship with Harthouse.
After almost running off with Harthouse, Louisa instead has a long and way overdue conversation with her father about the way he screwed her up. Afterwards she falls ill, and wakes up a sort-of new woman. Louisa permanently separates from Bounderby and forgets about Harthouse. She then makes up with Sissy and tries to help her sister Jane not become like her. In general, Louisa starts to rediscover the humanity she's been forced to repress.