To the OP:
I'm a parent of several kids...some in college, some graduated, and some who passed on college altogether. I won't get into the aspects of whether or not you have a right to spend your own money in a way you see fit...every home has different rules and the rules in your home are none of my business. However, I think some tips for obtaining the support of your folks may be helpful here.
If one of my children came to me wanting to purchase a new computer (yes, even with their own money at age 17), I'd be much more likely to support that purchase if the child had an important or value-added purpose in mind for that computer. The computer (and may Steve Jobs have mercy on my soul for saying this

) is a means to an end, not an end unto itself.
For example, one of our younger sons (at about age 17, as I recall) came to us about three years ago with exactly the same request: wanted to buy a laptop computer. However, he did not start the discussion with the need for a computer. He began by explaining he wanted to start a custom T-shirt business during his senior year of high school. He then laid out a business plan for the operation (a project from a business class taken in his junior year). Then he brought up the need for the computer to fill design needs (company logo, T-shirt designs, that sort of thing). He already had the computer picked out and explained why that particular computer was the best choice for his needs. He sold me...to the point that I bought the computer and suggested he keep his money to fund other areas of his startup. BTW, the business did great for a year - he wrapped it up when he left for school.
Shortly afterwards, one of his sisters approached me with a request for a computer. Her basis was "I want to surf the web, manage photos, burn some CDs...and, besides, it's only fair because you just bought one for Joe". No sale. When she came back in another year with more compelling and urgent needs, I supported her computer purchase as well. See the difference?
Your folks are just trying to do what they think is best for you, so don't be too harsh on 'em. Sometime we parents get it right and sometimes we get it wrong (wish children came with user manuals), but we usually have good intentions at heart. If you think out your compelling needs for a computer and lay out a well-thought-out request in front of your folks, they're more likely to support you in your purchase...regardless of when you decided to buy.
Hope this helps!