Do you mean that you're a high school student, and your card is one of those ones that is co-signed by your parents, or a college student under 18, or...? Anyway, this is what I would suggest, but it might need your parents to talk to the CC company on your behalf and not just you, depending on the circumstances...
Call your credit card company. Many of them will offer temporarily enhanced limits to allow a person to make a large purchase. Perhaps you can mail them the money (a check for the rough figure, to be deposited into your account, as if you were paying an existing balance) *before* you buy the computer.
EDIT: What PlaceofDis said while I was typing is really good advice too.