Getting back on topic...
Hi! I've been watching this topic since yesterday, but forgot where the log on button was <_<
Honestly? I'd print out a list of your preferred build, from NewEgg, and then show it to your parents. Make sure it has EVERYTHING (speakers/mouse/keyboard/monitor/OS, anything that you don't have a spare of), and make sure it's a low enough price where you know that you can convince them. You can always add $50 on, but the low price is a BIG bargaining chip.
Now, if they don't like the price, just nod your head like you understand what their hesitation is, and continue. If they're approving so far, smile and continue. Point out your reasoning for having each one. DO NOT, I repeat, DO NOT get technical. A simple "This will help me do..." and a "This is better than our current PC because this one..." will get it done. You haven't confused them, and you've justified your reasoning. If they ask questions, answer politely. Remember, you want them to give you $400+ to build something YOU WANT.
Then, ask them to take you with them to your local Circuit City or other store with a reputation for supposed "technical expertise" (Everyone knows this is the best place to go
), and show an employee in the Computer Section, ask what they think of the list. Ask them if there is anything comparable to that in their section, for that price range. Again, remember to be polite. Don't argue, but if they're giving you a hard time about a choice you made, try to correct them nicely, say, "Oh yeah, that's right, but...".
Finish up by asking if you can do extra things around the house, or (if you have enough money saved up one way or another) ask if you can pay for a portion of it (1/5, 1/4 or 1/3, depending on the price, is a good way to go.). Even if they say no to you, they realize that you're serious about this, and you really do want to do it.
Don't try to do this all in one day. It will take some time to whittle them down, and more often than not, spacing it out makes it seem more like a passion than a desire.