Stay in her room ALL DAY when she is 4? No wonder she's picking the paint off the walls.
First of all, I agree with Diane and Hummingbird. She wants attention and let her out of her room.
Secondly, in hindsight, (my oldest is 21) I can say that stuff like that DOESN'T MATTER, and I wish I'd never punished my children for toddler behavior. I remember one time getting all upset when my oldest was 5 because he had poked his fingers in some caulking that was drying on the sink. He was 5, and that stuff DOESN'T MATTER! When your kid is 21, you realize just how very, very young 4 and 5 year olds are.
Let her color on the walls, and pick off the paint. When she's 7 and stops doing it you can repaint her room. Who cares, it's her room. (And by the way, I'm an interior designer, and love a beautiful house, and I still say this.)
And don't put a 4 year old in her room all day! She's lonely and bored, that's why she's picking the paint off the wall!
Life is short, and one day there will come a moment when you realize that all that small stuff you fretted about is trivial. Paint, schmaint, you're gonna die one day. Don't waste your and your daughter's time together fretting over paint. You know the saying "don't fret the small stuff"? This falls under the category of small stuff.