If all else fails, simply purchase a new product key on eBay. (It won't break the bank!).
Make sure that you know which version of Windows 7 you've got. ('Professional', 'Home Premium', etc). If you're not sure, click on the Start button, right-click on Computer and select Properties.
Then search on eBay for a product key for the correct version. Such product keys have usually been extracted from scrapped office computers which were never connected to the internet (so they were never registered online with Microsoft).
This trader (with 99.2% positive feedback), for example, will supply you with a product key for Windows 7 Home Premium for £3.29
https://www.ebay.co.uk/itm/INSTANT-Windows-7-Home-Premium-KEY-32-64bit-Win-7-Activation-Product-Code-FULL/273236361620?hash=item3f9e280194:g:60sAAOSw95lbCBRP
(You can ignore the bit about downloading an ISO file. You don't need it because you've already got an installation disc).