Well paint me crusty cause i.m a parent and i understand where they are coming from.
With that said have you made a serious attempt to trim all the fat off of windows xp? I mean A serious attempt there is a ton of crap in xp than can really bog down gaming but otherwise let normal internet work fine. When i was active in this clan before i was playing fairly well with an amd 950 gforce2 64 with 256 ram and my only hang-up was a 28.8 dial up connection and that was with 98se. once i got a decent connection i was able to do very well indeed but shortly thereafter i got a major crash and burn with the comp and some other things as well. Maybe your parents know something they haven't let you in on yet you are 15? well it's entirely possible that they may be planning some kind of ride for you in your future and know that you will need the money for that? the main thing is they are your parents and yes it is your money but they could be trying to help you manage it a little better than you are willing to do for yourself. Been there done that got the mountain of debt to prove it.
but the best way would be is to try to get a part time job, take on a little more responsibility around the house and, yes I know it's tuff, but cut back a little on the comp time and they may relent when they see that you a willing to make and extra effort to not blow all of your cash in one load and have a plan to continually replace it with more not just a lump sum with one sale. Not to mention that it will also help you with convincing them that you need your own vehicle to go to work etc... once you have that steady income from a part-time job you will have a much easier time of convincing them to allow you to keep say 20-25% of it to the side to spend on a new comp. Parents are funny about wanting to see that you can function in a semi-realistic adult manner successfuly before they let you do other adult type thing like make large purchases that could make you nearly bankrupt. try impressing them with your adult capabilities before you try to make them let you make adult decisions. it's a strech and it's not the easiest way but that is how most of the real world functions you have to prove your worth before you can collect what your worth.