How can I help my father, who has been diagnosed with Alzheimer's, severe depression & Secondary Addison's disease, remain active?

My father is 77 years old. Seventeen years ago he had open heart surgery. He immediately quit smoking, cold-turkey, and walked 3-miles faithfully each day up until this past March when he started noticing changes in his health. He began losing weight, going from 145 lbs to 118 in just 6 months. After many doctor visits, numerous tests (chest x-rays, blood work, CT scans, MRI's - you name it, he's had it) and hospital stays he was finally diagnosed with Secondary Addison's Disease (adreanal insufficiency). He was prescribed Cortef and will be on it for the rest of his life. Because of losing so much weight and muscle so quickly, he became almost immoble, needing assistance to do almost anything. He also became incontinent.
As a result of all this, and partly because of the Addison's disease, he became severly depressed. This was a man who went from always being busy - gardening, yard work, home improvements, etc. - to physically not being able to do anything for himself. He has given up and doesn't care about anything.
Up until about 2 months ago he was living at home, but when he was unable to walk to the bathroom on his own (even with the help of a walker AND family members we had to put him into a skilled nursing facility for rehab. The idea was for him to receive therapy until he was strong enough to return home. Unfortunately he either refuses outright to participate in therapy or only puts forth minimal effort when he does decide to participate. He's severly depressed and has basically given up.
He was first prescribed Lexipril for his depression, then Welbutrin was added. The Lexipril wasn't working and Welbutrin caused him to have tremors so bad that he couldn't even feed himself. He was taken off both and put on 20 mg of Prozac, but we noticed no change in his mental state. The dosage was increased to 40 mg, and still no change.
All he does is eat and sleep (his appetite is excellent because he is on an appetite stimulant). He refuses to to anything to exercise his brain - won't read, do crosswords or any other type of puzzle, doesn't care about TV, won't participate in any activities the nursing home holds, and when we ask if he wants us to push him down the hall in his wheelchair he argues with us or refuses. We visit him daily and he has many other visitors throughout the week, but he just sits silently or closes his eyes. He only talks when asked a question, and even then it's "I don't know" or "I don't care."
It's hard to tell what stage of Alzheimer's he is in as the physical limitations that have come from his other problems are confusing the issue.
I guess my question is, how do you keep a person with Alzheimer's active, both mentally and physically, if other conditions (depression, Addison's, etc.) are preventing the person from caring or wanting to do anything? Has anyone else had to deal with a similar situation?