Absolutely, it is possible to train your dog that certain areas of the house are off-limits.
I, for example, don't allow my dogs in the kitchen (not ever, because that's where I fed my cats) or in bedrooms (unless invited). Here's how my experience of training my boxers about the kitchen went - it was a room a little like the one you describe insomuch as it had an open doorway (no actual door) to the dining room. There was a second doorway too, on another wall, but that one did have a door.
Anyways, for the first couple of weeks after bringing my new puppy home I put a small baby gate across the "insecure" doorway. Any time my puppy showed any interest in going there, I just told her 'no' and called her away (lots of praise as soon as she responded), then
engaged her attention in some other activity - usually a game or a short training session, occassionally just one of her own toys. After a couple of weeks, the baby gate came down but I continued to treat the doorway as a barrier. It probably helped that that was the room in which I prepared her food - because I'd have her sit just outside as she waited for it. If she made a move to enter the room, I was right there with an 'Uh uh' to mark the behaviour and to put her back in her 'sit' (praised). She caught on very quickly - there was an 'invisible' barrier right at that doorway
I think a defining moment came when she was about 3 months old, when we were playing a game of fetch indoors. Well, I threw the ball too hard, it sailed through the dining room with puppy in hot pursuit, and bounced right into the kitchen. Well that little puppy paused, and glanced back at me - a moment I seized upon to call her back to me. She came running, and was praised like she'd just won the lottery LOL (I went and got the ball, of course, and our game continued afterward so she was well rewarded).
But that really was a defining moment for her - she'd "got it" that the kitchen was out of bounds. LOL I don't think she ever set paw over the line again, even if others tried to tempt her. Obviously, I always rewarded her for resisting too
She was a crate-free puppy with free run of the house by the time she was six months old - no damage, no chewing, no accidents, and no stealing the cats' food from the kitchen
I did exactly the same with Henri as a puppy. He had the benefit of another dog to 'show him the house rules', so also learned very quickly. He didn't have quite the same concept of the 'magic line' he could never put a toe across (here's a
pic of them waiting for their dinner - and you can see Henri not only has his feet in the kitchen but his eyes firmly fixed on the cat food to his left LOL). But he still never went into that room, and he never raided the cat food either. Given that I left the cat food down all day every day for the cats, he certainly wasn't without temptation.
So yes, it certainly can be done
The key is establishing a 'boundary', ensuring that the dog
understands what it is you want, and going overboard with the rewards and praise when she complies with that. And that needs to be ongoing
Here is a recent thread that discusses a similar situation. Julie has attached some very good links in here that you might find helpful
http://www.boxerworld.com/forums/showthread.php?t=65029
Just as a final note, since it is a place with 'dangerous' items, I really would see if you can find a way to attach a baby gate (or a couple of them) to block off the entry to that room. Not very scenic, I know, but even if it isn't a dog-proof barrier, it would help to reinforce the 'boundary' line you don't want her to cross.
