Accept he has HIV, you can't change that.
Depressed people may not listen even if they say they want to pick themselves up, they feel ashamed or helpless if they try to.
From a strategic management perspective, you can't change a persons paradigm without being a little forceful.
Stories
Symbols
Structures
Power Structures
Control Systems
Routines and Rituals
(who says I didn't learn anything in my BA hons^^)
Look up the cultural web online, and find out what each of those mean, identify what your brothers are, then find the ones which are influincing him into this depressive state. Often you will have to break through and stop him from talking about the past (stories) and get talking about things to value now and the future. Literally kick and persuade him out of his routines once in a while, more often. Find out what he feels he's being judged by or factors that stop him being proactive (control systems) e.g. public/family opinion and make arguments to ignore, change his perspective of what their real opinion is and actions are for, reduce the frequency with which he is put under that situation etc
I'll leave the list at that
hope it helps.