Can I make a new install for an OEM machine?

[Nathaniel Herr]

I'm trying to fix up a laptop for a friend of mine. I pulled the product keys and then wiped the drive. I found out however that there is an embedded key on the computer. The original disk and anything else that came with the laptop is gone, can I make an install on a usb to have a key that matches the one pulled from the machine?
If this isn't doable then will I run into problems trying to buy a new install? When I tried to install a backup of windows 8 I had it never prompted for a key stating that the one I had was invalid.

 

[Phillip Corcoran]

"I pulled the product keys and then wiped the drive".

Bad move. There may have been a hidden factory recovery partition on it, you don't need to enter a Product Key for that.

 

[Nathaniel Herr]

"I pulled the product keys and then wiped the drive".

Bad move. There may have been a hidden factory recovery partition on it, you don't need to enter a Product Key for that.

It was so horribly virus ridden I decided to destroy the flash drive I used on it. I could barely get task manager to respond in the first place.
Using any backup wasn't an option at that point.