This reminds me of the fairly famous quote. 'Teenagers, Tired of being harassed by your parents? Act Now!! Move out, get a job, pay your own way, while you still know everything!'
All the passive aggressive crap in this thread is sickeningly amusing. She has the right to believe that it's a family resource (which SHE would have ultimate control over), rather then something that explicitly belongs to YOU. As I see it, it's being used as a pawn in some sort of power struggle. You never once mentioned WHY she is threatening to take it away, and you're so caught up on the 'she's trying to take away something that belongs to me' argument that you're not even LOOKING at what she is trying to say.
As a few people here have noted, she would be perfectly within her rights (unless you have an actual agreement to pay rent, at which point it becomes stickier) to dump you on the street with just the shirt on your back. It may be a ***** thing to do perhaps... but it's still within her rights.
Yes, you may be 18 now, which can give you the legal right to own property. However, from the impression I get, the upgrade process on the computer took place over a relatively extended period of time... over a couple years. Before you were 18, anything you bought became property of the family, not to you personally.
Somehow, as I see it, usage of the computer is being utilized in a way similar to... say, usage of the family car. The parents own it, though you as part of the conditions of you using, you may be required to pay for portions (the details of which varies according to the family) of the maintenance. If you fuck up something or other (which it sounds like there's a very good chance you may be doing), they would be within their rights to take away driving privileges.
Now, to the rest of you. The vast majority of the comments seem to involve 'take out what's hers, and give her the rest.' I'm sure it doesn't take a rocket scientist to see that whole line of action is counterproductive, and will only make whatever is causing this situation worse.