Sounds an odd situation - he wants to get involved, comes along but can't engage. So, has he always been like this? or is it more recent?
If he has always been like this, it sounds as if this is something about his personality or temperament which is going to be difficult to change, even if he wants to. I am not sure why your friends find it too difficult to include him if he is just sitting there - granted, that is not ideal, but he is not being abusive or aggressive, can't they just accept he is a quiet one and maybe just smile encouraging at him once in a while?
It's the same basic problem underpinning so many relationship difficulties. You are not happy, he isn't acting in a way you want. So you can either try to change him (talking, counselling) or accept the situation and do things that make you happy even if he can't or won't join in.
I agree with other posters, it is helpful to write down what you want out of life, what do you enjoy, what are you good at. I can't remember who said this, but it was someone famous, who said that happiness requires someone to love and something to do. It may sound trite, but volunteer work, respite foster care etc, etc can give you a focus away from your own unhappiness and a sense of purpose and perspective that can be very valuable.
It sounds to me a little as if you are making him the focus of all your unhappiness which isn't fair as it is unlikely to be true.