Harsh... Yes.... But, sometimes you gotta be cruel to be kind.
Does your house have a TV? Does he pay for cable or similar?
Perhaps he's already paying for whopping great globs of bandwidth and is concerned about your "Addiction". (I quote your avatar Sirricharic)
I wont delve into the reasoning of parents. I am one and trust me, we have our various reasons for all we do.
Usually its for what we
believe to be best for our offspring. (Even if, no-one is correct all the time)
I can only guess at why they've said no. There could be many reasons.
ie. Do you have a birthday coming up?,
Can they actually afford it? when to them it may seem as yours is fine,
Is it YOUR computer, or the FAMILY'S unit? (Is your machine already better than the family unit?)
Fair to say that most parents want more for their own kids than they had themselves. Also fair to say, I bet you do have exactly that.
That said, you did come across as a whiney spoilt brat. That in itself shows you have some maturing to do. Which may very well be the lesson you're meant to learn.
I believe I speak for most parents when I say that we react much better to a more disciplined approach than just saying "Gimme Gimme ... WAAAHH!!"
Evidently, you are a clever young man. Act accordingly. They will more likely encourage this than refuse it. But, they may simply not understand the relevance/importance of a "better" machine. (as it is with most older people.)
Seriously consider 2 things... 1: Performance Upgrade. (its cheaper. (I bought recently a 2 yo mobo with quadcore
support and DDR2 ram for $85-) and its the "clever" and reasonable option)
2: Use less intensive software. It is out there. And works just fine for training and display purposes.
Only for the time being of course. Until you take over the whole world, later...
(I may be able to help you with point 2. If you ask...)
I still stand by my earlier comments ...
Set yourself a goal... and ... WORK TOWARDS IT...!!!
Honestly, I applaud that you want it for a good reason like CAD work.
That's what I do...
I get good grades but they don't want to help me out at all. My parents won't even let me wash their car or do laundry for money every thing I do at home has to be for free or I get forced to do it I'm not saying I want them to just buy me a computer for nothing they don't even allow me to work for it.

Getting good grades is it's own reward. Stick at it... And, you ARE supposed to help around the house anyway. You live there after all. Plus, it shows maturity and responsibility. These attributes put you closer to "on par" with the adults around you. You may find yourself therefor being taken more seriously...
Rant OVER... Lol
