Hi HM, I know you are tired, but it's going to take some perserverence in order to get things to change. The one good thing in all this is your recognition that you do have needs...you need this man to offer you emotional/physical support.
Besides his lack of desire for sex, there is an atmosphere of negativity/criticism and lack of affection. There's the "emotional fusion" of marriage along with H's underlying depression. It's gone on for so long, and with work and 4 kids, no wonder you're exhausted.
I have been working on many of the same elements, and I have to say, MM's concept of "dog training" really helped me. You still love the dog ( your H) but not the behavior. You have to detach and call him on his actions, in a strong way, with no apologies, and then get back to yourself. Try not to linger in emotional distance after each interaction ( hard to do when the attacks become personalized). He has to know that you will no longer tolerate his excessive negativity and that you are strong in your resolve. The quicker you can get back to yourself, the healthier it is for you...and for him. The hope is eventually he will begin to see that his attitude is "off" and is that he contributing to the difficulties.
While you are limiting the negativity, you also have to add in positivity into the equation. Set up a schedule for hugging ( maybe before work and after work) and a time for the two of you to have fun without R talk. You are consciously adding "affection" back into the picture, even if it doesn't feel so natural to begin with. Sometimes emotions follow behavior.
Lastly, I do feel you need to confront the sexual desire issue, but I would wait until there is a better feeling between you, when the affection clearly outweighs the criticism.
Remember in all this to take care of yourself---do things just for you!