New
#11
I seriously doubt that both computer are exactly the same.
They would have to have the same motherboard signature and bios.
They would have to have the same COA key for Windows 7; which they shouldn't.
Because you don't seem to have backups or clones of your original system before your drive died, the best option would be a Clean Install of Windows 7 on a new drive using the COA key on the Microsoft Sticker located somewhere on your laptop. All you special settings and programs would have to be done anew again.
You could just save your damaged drive and try to recover your data from it once your system is up and running properly.
Edit:
If you did get to use your recovery partition on the damaged drive all it would do is put your compute back to the way it was when it was made, therefore you would of lost all your special setting and programs.