How can there be no punishments for bad behavior?
Are you saying that you never provide consequences or "punishments" for inappropriate behaviors?
Traditional parenting tells us to mold their behavior.
But traditional parenting is very concerned with how well the children appear to others and how convenient the children are to live with.
To me the primary concern should be why a child is behaving as she is, not what she's doing. If a child is lying or stealing or hitting, there's a reason behind it. Stopping the behavior doesn't stop what's causing it. It just forces the cause into a new channel.
If we see kids as inherently bad who need to be taught to be good, then punishment makes sense, I suppose. It would be like pulling weeds. But I see "bad" behavior as either not understanding how their behavior is affecting someone else, or because they aren't yet able to understand, or as a reaction to how they're being treated, or personality. (Slamming a door is a lot better than punching someone!) Accepting that their needs are different than ours -- because they're kids and because their personalities are different than ours -- is often hard, but it's a pathway to being their partner rather than their trainer.
My question is, what now? Do I have a heart to heart with my daughter, and tell her there will be no punishments from me any longer? She no longer needs to brush her teeth, or clean her room?
I think that you're seeing two choices: either you make her do the right thing or you let her do what she wants. And since what she wants may be the wrong thing ... then what?
Try being her partner instead. Maybe, in this regard, think of her as a friend in order to help you see the difference between molding her and helping her.
Presumably she doesn't want cavities. But she doesn't want to brush either. So what is it that's getting in her way of brushing? Does she object because it's another one of those things that's always been forced? I know as a child I remember brushing teeth taking a good half hour all by myself while there were way more interesting things I could have been doing. Obviously it only took 60 seconds ;-) but it seemed like half an hour! So I've always brushed my teeth with my daughter. She's old enough now that it's pretty much an automatic thing so she doesn't have to devote much consciousness to it, but doing it together got her past the years when she was hyperconscious of the tediousness of it.
Also, what about when she slams that Playstation out of frustration. Just sit and wait - if she breaks it, she pays for it?
Again, presumably, she doesn't want to break the Playstation so, say that to her. Talk about your concerns when you're both doing something else. Say "I'm concerned that taking out your frustration on the Playstation may break it one day. Is there something we can think of that you might bang or throw or do to release the frustration? Something we can keep right next to the Playstation?" Perhaps ask her when she starts to play what strategy she'd like to use if she gets frustrated. (And talk again when she's not playing to see how it's working and whether something might work better.) And then when she does bang the Playstation, humor helps as someone said. Saying "The Playstation says Ouch!" and then hand her something else to punch. Talk to her when she's not in the midst of playing about what her feelings are before she gets to the need-to-slam-the-Playstation feeling so she can become more aware of the buildup and redirect it before it gets to that point.
Assume she will unthinkingly slam the Playstation until she's able to insert a moment of thought in there. It's a retraining as well as a developmental issue. And you'll have to accept that she's going to do it wrong until you and she can figure out a way that works for her.
There needs to be basic, considerate rules. For instance she can't throw things at the big screen tv, and can't color on the walls ...
Again, what's leading up to it? Help her become more conscious of what she's feeling and find new releases.
Why is she drawing on the walls? What about a big sheet of paper? What about a wall she can color on?
There aren't rules in our house. We're just guided by what makes sense. If your daughter is feeling controlled by the rules, it's possible she'll choose not-sensible things because she's fighting the inability to make the choice for herself and not because she wants to do something ridiculous.
There are some communities that have rules about what colors you can paint your house and whether you can have plastic pink flamingoes in your yard. Being rather conservative, our house has conservative colors and no pink flamingos. But if for some reason it turned into one of those controlled communities, I'd have great desire for purple woodwork and plastic pink flamingos ;-)