Here's how I'd do it.
Connect the drive to another system.
Open regedit on your PC as administrator.
Click on Hkey_local_machine
File > Load hive
Browse on the other drive to windows\system32\config
Select "Software"
Give it a name like "Software2"
Browse to
HKEY_LOCAL_MACHINE\SOFTWARE2\Microsoft\Windows NT\CurrentVersion
ProductName will be what it is, pro, enterprise, home etc.
When done, highlight software2 and then File > Unload hive. (important)
(Note you may have to manually browse to regedit.exe, right click on it and select "Run as administrator" for it to work right.
Now the only think left to figure out is if it was OEM or Retail. If the sticker is on the computer, it is surely OEM, unless they did an upgrade pack to convert from Home to Pro like I did on my laptop, but I have the key for that saved luckily.
If the laptop was one of the non-business brands (Not Dell / HP / Lenovo) that you'd normally buy at the local computer store, it most likely has the Home version of Windows