I'm a step-grandma. My GS came into my life when he was 5 and my son formed a relationship with his mother (the boy has a father and other grandparents who don't want to know).
My advice is to take things very slowly at the child's pace.
Don't force the 'grandparent' thing on them, just allow them to see you as a loving, caring person whom they visit.
Discover what they like doing and invite them to participate.
My GS was invited to help me bake and he accepted - and there would have been no comeback whatsoever had he refused. We now bake regularly and he often asks if he can cook when he visits.
I personally dislike that 'step' bit - when my GS is introduced now, it's as 'my grandson' and at 9, he calls me his grandma - but I never asked for that, or even suggested it, it came entirely from him.
Before, he was introduced by his name, and sometimes still is.
If he had wanted to call me by my given name, that would have been fine.
Older grandchildren often want to do their own thing and if they simply sit and look at a screen, I'd still try to find out what they liked and if it meant asking them to show me how a game worked, or watching their chosen DVD with them, at least I would be showing how happy I was they are with me and letting me share.
I think the key word is time - give them time and spend time with them.
I once read about a father who took his son fishing and they were sitting on the riverbank, in absolute silence, so the fish were not disturbed, when, after two hours , the boy tentatively spoke about being bullied at school. He needed that time to feel safe, and constant chatter at home had not given him time to formulate his ideas and words.
Sometimes just being there and allowing the silence and companionship to bond you, is all a child needs.