Oh my goodness, what a little cutie (ha ha) she is!
It's wonderful that you adopted a kitty who'd been at the shelter so long.
I've been considering adopting new kitties, and I've been looking specifically to adopt kitties who've spent a long time at a shelter. It just seems so sad that they've spent all this time in cages.
I'm not at all surprised that she won't come out. After 4 years in a cage, she probably feels safe in there. I would put her food, water, and litterbox in the room with her and then leave. I'll bet when you get up, she'll have touched at least one of them.
I would also not push her to come out before she's ready. Maybe just sit in the room with her, doing your own thing, and not trying to get her to come out.
Please do keep us posted! Once she gets adjusted, she'll probably be a totally different cat!