What's the difference between mental illness, a broken spirit and demonic possession?
There is no difference. All are problems from the human mind.
Mental health issues can be fought through affirmations and natural tools to help realign your thought processes.
Talk therapy is, of course, highly useful in the treatment of many mental health problems, but sometimes the patient needs medication as well. Schizophrenia treatment, for example, will go nowhere if the patient isn't properly medicated.
I agree with JeanP that this sort of nonsense can harm the mentally ill and should therefore not be encouraged by Christian charlatans.