So I purchased the Windows 7 Home Premium for only $30 (student discount) but they only really gave me an EXE to upgrade with, which is useless for running bootcamp. But my friend bought Windows 7 Home Premium for the full price and I was wondering if I would be able to use his disk but my product key?
Yes and no. You can install with his disc. If you are installing on a Macbook with a virgin bootcamp partition, that being that you have never had an install of Windows on that computer, your key will not work.
Install with your friend's disk, do not put in your key at the end of installation. Instead, complete installation and open Windows 7 (it will be in "Trial Mode"), complete the steps in this tutorial:
click here, restart, open Activate Windows app, enter your key and you are done.
This is the method I used to great success!