There is a program called
Keyfinder that allows you to find the Windows or Office Key off your installed computer if you need it for re-installation purposes. I'm not sure if it will work if you copy the windows directory as you mentioned.
You could also try copying the windows registry from the non-working computer to a working computer (this might screw up the working computer completely, but if they are both the same kind, and working in safe mode work)
From DOS, on the C: of the working computer, with the non-working windows installation as the slave:
Attrib -s -r -h C:\Windows\System.dat (or depending on the location C:\Windows\System32\Config\System.dat) and
Attrib -s -r -h C:\Windows\User.dat (or C:\Windows\System32\Config\User.dat)
These two files are where the registry is held, and doing this will remove the read-only, hidden and system file attributes from the registry files.
Copy these two files into a safe location so you can restore the working computer back to it's original state once you get the cd-key you need, or if the entire process completely fails.
Then proceed to copy the old registry (User.dat and System.dat) from the slave drive onto the C: drive (on the slave drive, the files will most likely in the same locations as mentioned previously in the other drive ie: D:\Windows\System.dat )
You could also re-add the attributes to the replacement files once copied onto the C: Drive( by replacing the "-" with "+" as follows:
Attrib +s +r +h C:\Windows\System.dat )
Then boot (safe mode is best} and pray...
(note, this is just a reasonable hypothesis from my experiences, and I do believe it will work)
Hope this helps, and good luck.