Ruby - I am not sure how old this young man is - I think that makes a difference to your decisions.
If he is still late teenage, then his being at home is not out of the norm; and his inability to empathise with you and your health problems is a pain, but might not be unusual for a boy of that age who is worried about his own life.
If he is older, then the situation is slightly different.
In either event I do not think you can have a say in what he does next with his life - I know you want him to go to uni, but if it is not what he wants then that has to be his decision. I might feel my DDs have wasted potential, but they have to choose what they do with their lives. I know you want him to "make something of his life" but in the end, as a young adult, it is down to him and no-one else to decide what he defines as making something of himself and to either do it or not. We can make suggestions, but in the end it is down to them.
What you can have a say over is how he behaves in your home. Are there any ground rules about helping with the housework, financial contributions etc.? You could simply stop doing the things he takes for granted - e.g. laundry, shopping, cooking unless he meets certain conditions of behaviour in relation to your shared home. I would also ask nina's question as to whether he goes out and socialises at all.
I would also suggest that young men are a high risk group for hidden mental health problems (and indeed suicide) - not trying to put the wind up you, but there is a possibility that he might be suffering in some way and that the facebook/games/youtube are a cover-up for feeling he cannot face the world.
I suppose that what I am saying is that, much as you would wish him to be/behave differently he has to make his own choices, even if they are ones you do not like. If he does not feel brave enough to venture into the world and stand on his own two feet, he can at least be expected to observe some basic ground rules at home - not rules that ask him to live as you want in terms of career and daily activities (e.g. studying as you want him to), but ones that give him the incentive to behave as an adult - i.e. taking his share of things that need doing and knowing that his life will be less comfortable if he does not. A gentle dose of reality: if you do not get the shopping/tidy the living room/wash some clothes then some of your creature comforts will vanish.
I do not know if you have ever read anything about Transactional Analysis - it is a theory and therapy that states that we relate to each other (whatever our age and whoever) in different roles - very often reflecting child/parent roles. Your son is still in a child role at a time when your relationship might be expected to be moving on to relating to each other as two adults.
Might it be worth your while asking yourself what actions you are taking that give him an excuse to stay in that child role? I am thinking that he is used to you saying the same things/expressing the same concerns/ nagging the same stuff (as he will see it) and he might be brought up short if you change your tack. e.g. I'm off out to the cinema tonight, you'll have to get your own tea, and, oh by the way, there's nothing in the fridge.
I do not know your circumstances ruby and some of the above may not apply (e.g. you may not be able to get out to the cinema or whatever) but these thoughts are intended to be helpful, so please take them in the spirit in which they are meant!