My mom bought me a Dell XPS (8300? Can't remember the actual number) before my freshman year of highschool in started for school, so maybe you can convince them you need one for school or some such. If you're looking at $2000 I assume your parents are well off financially, so maybe just a nice stock desktop that you can upgrade later could be an option.
I'm all for working and such but sometimes it's nice to get a headstart, I would've missed out on Arma 2 DayZ mod back when it first started, minecraft when it started, hours of modding skyrim--
It definitely threw some lessons at me to, regarding viruses and getting rid of them (formatting my harddrives, getting my setup hijacked by some guy in russia or something, etc. etc.)
I believe the younger you can get a computer into a childs hands, the more they'll know through self teaching, atleast for me that's how it went.
I'll probably end up having a kid at some point and do the same thing my mom did for me!