Why will my grandmother, who is capable of speaking and cognitive, not answer me?

I agree with Boz. As we get older, sheer exhaustion makes us not want to talk if we don't have to do so. My father didn't want to talk to my mother very often, but told my teenage son, who sat with him at night, memories about WWll that no one else had heard before. I often kept my conversations to a minimum with Dad, but he loved for me to come to him for advice. Boz, you are right about the need for self worth. My mother and I have an agreement to look after each other even though I am 27 years younger, and I truly appreciate the things she does for me. Animals are a gift to withdrawn people who love them. I have been ill for two months and my dogs are a huge part of my recovery. The only thing that concerns me is the question of illness. Does your mother have any new medical concerns? That might be the real reason for her lack of interaction. Take care. Rebecca

She sounds angry, unhappy, bored, and lost. If all else fails try a child, a baby animal, something that is hard to resist to get her to open up. See if you can find something she can help you with so that she feels a meaning/value in life.
I had my father watch my youngest son after school for 1.25 hours a day rather than place him in after school care. My son and he watched t.v. together. My son helped him put a snake together that they shared. It saved me a little money which meant a lot to my father...to think he was really helping us out. The time they spent together was precious.
Sometimes feeling needed and valueable makes all the difference in their self worth and relates to how they respond to the rest of the world.