Heya... I don't really know what to do in this situation.. but I got a few ideas.

Can't you try to communicate emotions with something else than words. From what you said, I'm actually doubtful it will work but it could be worth a try. You could try to use pictures of human facial expressions. A lot of people love using smileys you know..

Rather than saying "What do you want from me?" you could try to say "Is there anything I can do for you?". Then...I don't know...if it was me I would probably say "No" but would highly appreciate a comeback like "Ok. But I'm just here for then like always ".... I hope you get what I mean.. xD

Depression can arise from all sorts of strange reasons. Some people just feel down and don't know why. It could be that he doesn't get all the nutrition he needs... minerals and stuff.

Myself I usually get a lot of anxiety when an exam is closing in...although I don't always feel that it is because of the exam I do feel this way... it is just a "strange" coincidence. For example I might feel highly prepared and don't feel like a "fail" will cause that much problem.. but I still get more anxious the closer it gets.

He could feel depressed because of an recent event even though he doesn't know himself that it is linked to it.

You probably already know all this but I just want to make sure that communicating emotions won't necessarily make you find the cause.

Wish you well..