As a sixteen year old, I can say I understand the frustration of having an outdated computer. I am barely able to play older games with decent framerates on the family (six siblings) 2001 Sony Vaio equipped with a P4 Willemette 1.6 GHz, 512 MB DDR (PC2300), and a GeForce FX 5200 (I actually bought this to play C&C Generals and replace my stock 64 MB GPU). Even other tasks such as webbrowsing and watching videos is slow due to this.
It really is a bummer when you're still under the legal working age limit, but despite that, I have managed to save $1500+ since I was 13. Plus, I have my own '95 Toyota Tercel (not from my parents ) and will be paying my own insurance once I get my liscence. On top of this I pay my own cellphone bill and gym subscription to Planet Fitness. I also have my own 24" TV and Onkyo 5.1 speakers with an Xbox and 15+ games. Everything that I have is 100% mine; I earned it. The reason for being able to save so much money and buy so many things was that I did hard manual labor with my dad and some of his colleagues instead of sitting around and doing nothing.
I am not trying to brag or point fingers to myself, but I want you to realize that it takes hard work and sweat to get what you want in this world. Take this as advice and start mowing lawns, pushing carriages, bagging groceries, or whatever else you can do, and work your way to that new hardware. Not only will this give you a sense of achievement, but one of pride and knowledge that 100% of your machine was earned by you.
By the way, a large part of my possessions comes through smart shopping. I've always been the kind of person to search for deals high and low instead of merely paying MSRP. Because of this, I have undoubtedly saved myself over a thousand dollars and been able to get more for less.