Does it have a "Fat cap"? That is, an intact layer of fat on top? If the fat cap is broken or it doesn't have one, I think 1 week is about the outer limit for broth. With an intact fat cap, I've been told it will last for up to a month in the fridge. I haven't made beef broth, and chicken broth's fat cap breaks too easily, so i haven't tested it, but that's what the chefs at the kitchen I volunteer at said.
I generally just make chicken stock but I will use it for up to a week. If it has a nice thick, unbroken fat layer like the PP mentioned, I've pushed it for 10 days or so with no problems but haven't dared beyond that.
I try to freeze it if I won't use it in a few days, but I certainly understand forgetting about it - it happens!
Give it a good boil & see how it goes. It's worth a shot not to throw out good stock. From my experience, instincts can be pretty right on about if something's "iffy" or not. I'd give it a go, maybe with beans or something that's going to boil for a while, just for the case of Carley related safety