If your cousin upgraded directly to the iPhone 3G, this would have automatically de-activated the first-generation iPhone. AT&T was sneaky like that, hoping that you would sell the iPhone or pass it on to a family member who would become a new subscriber.
You don't need a SIM card at all to unlock it, but unlocking instructions could change slightly depending on the firmware it's running. You can check the firmware version using
this tutorial. Tell us what firmware it's running and we can point you to a PC tutorial on how to unlock and activate it.