Just to be clear, are we talking about the EXTRACTED key, using a utility like Magic Jellybean, or the product ID, as listed in "System" in control panel?
key extracted through jelly bean. not the product id
i did not bother comparing product id's since they have never really been important before so never got in the habit.
edit: and another side note, i have read a lot of people having issues deleting windows.old folder after the upgrade. it is locked by the system it seems. you can get rid of it as well as the update files through the "disk clean-up" utility. search it on the search bar. then at the bottom of the window that opens, there is an option for "clean up system files" and then check the boxes for old installation and temp files and this will get it all out for you. been saving about 15-20 gb for me so far this way the few times i have done it. thught i'd share snce i have seen a few posts about this.
Yep. The system cleanup or use of the "take ownership" script to add right click permission changing, and then taking ownership of the windows.old folder, are the only two ways I'm aware of that are working to remove it.