I would doubt it. Usually the free credit card offer they send out to college age kids only come with a small limit as the don't know if they can trust you - $500 and under.
I ran into this problem to. I never needed credit. Even for a car, I simply saved my money, and paid cash. So for being financially responsible I got punished when applying.
A few years back I applied for a credit card at a regional lumber yard and was denied. I was looking to run through maybe $15K or so in the next couple years as I built a 4 stall garage and shop on my parents house. So instead I had my parents (who have good credit) sign up for a card and then sign me on as a authorized user of the card.
Because I am an authorized user on this card it shows up on my credit history. Although most of payments run through this card were mine you can accomplish the same thing if most of the payments are actually your parents. From this I was able to get a $15K VISA card.
Just be sure your parents don't make late payments on the card - you are a authorized user and their failure to pay on time will show on your credit history, which is the opposite of what you want to do (I was lucky in that respect). Send payments via the internet or mail EARLY - don't wait until the last minute. And be sure to save your money if you buy under a program which allows you to pay off the balance in 12 months with no interest - don't keep thinking well thats a long way off - make sure you save a lot of extra $ for unexpected expenses. If you can't plan long term don't do it, you'll only screw up your credit long term.
Also, is there a specific reason why you need a computer for college? Are you doing it because everyone else is? I went through college with a 3.84 (4.0) GPA (during which I worked and started a small business) and I am not a rocket scientist - I did it without a computer. The best computer you can have is a pencil and a 70 page notebook.