Re-installing w7 on the same laptop with new hard drive?

Bought a Gateway laptop 3 years ago. I used it for 3 months and then it fell off of my bed onto its screen which destroyed the screen. (3 years later) I just bought a replacement screen and installed it. It works perfectly, BUT I find out that my hard drive is dead . I ask a professional and he said to buy a replacement hard drive and re-install windows 7 home premium using the product key that is on the underside of my laptop. He said to either borrow someones windows 7 install disk or to use a flash drive.

I figured out how to install windows 7 from a usb but through my research i also found out that the key on the underside of my laptop doesn't work for everyone because it came pre-installed.

Someone also told me that it should work since I'm still using the same laptop, even though i changed the hard drive. That it will recognize that my laptop is the laptop that originally used that key.

I'm SO confused right now and I feel like giving up! I just need someone to guide me in the right direction. Should I just go for it and try to use the same key? Or is my only option buying windows 7 all over again? Help please!