Have you tried making him your "special assistant"? It will build his self-esteem, keep him glued to your hip, and enable you to work with the rest of the class at the same time. Provided the child is not ADHD, this could be a feasible solution for you.
Just have him pass stuff out, sharpen pencils, etc. Invent stuff if you need to, just make sure that whatever it is its "important" and gives him the illusion of some control. Continue to offer positive reinforcement in the form of praise at every opportunity.
If the child is abused, this may be the one and only place where he does get any positive attention; he may be very needy.
Do your best, but be prepared for the idea that the boy may need more help than you can provide like counseling and a safer/more secure home environment before he is able to modify his behavior.
Consider asking a counselor or licensed therapist for advice as well.
Good luck and prayers your way. Giving up on a kid is never a good feeling; I pray that you won't have to.
*edit* PS---Even if you can't "fix" the situation, take heart; you should know that whatever kindness and love you show this child, your patience with him, and your good example may very well be something that he will remember fondly for the rest of his life. So everything you are doing, even if you do not see immediate results, may make all the difference in the world to this child.
I know. I was a troubled child in 3rd grade as well, and remember some love and kindness showed to me as well that carried me later in life when I thought I was worthless.