I'm guessing that you're not old enough to have a part time job yet, otherwise I'd suggest that you'd just save up and buy it yourself. The upside of being an adult is that you can buy your own stuff. The downside about being an adult is...well, THAT YOU HAVE TO BUY YOUR OWN STUFF.
In terms of reasoning with your parents, the "keeping you off the computer" would probably be a good idea, but earning it (ie: paying it off in the form of extra household chores, odd jobs) will go a long way to getting your parents to get it for you, as opposed to having your parents just GIVE it to you.
If you are the one that put in the work towards getting the stuff you want, then it will show your parents that you put more value in it, as opposed to if they just get it for you (plus, parents think that their kids will take better care of their stuff if the kids put in the work). That's what grown-ups call "taking ownership."
Just a warning, though. Do not just suddenly start doing the dishes or cleaning your room more often. This will only backfire, in that they will just expect that the dishes and your room will be clean more often. Make your intentions and your expectations clear, but be nice and polite about it.