Depression is hell, and it's common for men to hide away from it by burying themselves in pastimes like gaming that don't demand much of them other than a bit of attention, I recognise his behaviour. That doesn't mean that it's ok for him to abdicate his responsibilities to you and your child though.
Playing computer games all day and chatting to online friends is a lot easier and less demanding than job hunting or going to college, but even if it's true that his lack of qualifications is hurting his job prospects, be honest with yourself. Has he actually applied for that many posts to begin with, and even if he does go to college, do you honestly think he'll dedicate appropriate time and effort to that when he's obsessed with spending all night in his online world speaking to his online pal?
Has he actually done anything to address his depression, or is he just hiding away from it in the hope it all miraculously resolves itself?
You need to find out what he's actually doing to deal with his depression, make it clear that his behaviour is not appropriate, his circumstances aren't tenable, and that there's no way he's going to be able to hold down a job or give a college course the attention it deserves when he's online 10+ hours a day and has a partner and a child to consider.
I think it's clear he either has no idea about how far out of line he is, or he does, and he either doesn't care, or is finding it far too easy to hide from his obvious real world problems by disappearing off into the internet all day and night. If you're not at the point where you're already about to walk away from him, then surely you need to spell it out to him in clear and concise terms where he's falling short, and exactly what he has to do to start holding up his end of the bargain.
You are not obliged to stay with him, it's clear you're unhappy, and I think you have to have a long think to yourself and ponder what it is exactly that is making you frightened to leave this relationship, because the way you describe him, it doesn't appear to be anything that your partner is bringing to it that is causing your reluctance to leave.