If you can read the windows registry file from your hard drive you can find and export the product key, and if the product key is for a retail(not OEM) version of Windows 7 you can download a disk image from Microsoft.
Find the software registry hive on your bad HDD located at %windir%\system32\config\software and load it up using a registry editor. I haven't done this myself, but there are some tips for doing so here
https://www.raymond.cc/blog/recover-...egistry-files/
Once you can search the registry you need to find the key named HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion and read the value named "DigitalProductId" and decode it using the tool at
http://www.ed.scherer.name/Tools/Mic...IDDecoder.html
There are instructions on the page, but you need to change the offsets for Windows 7. Instead of grabbing the bytes at offsets 0034 through 0042 you need to get the 16 bytes at 0044 through 0052. Copy those hex bytes and use the tool on that web page to decode them and get your product key.
Once you have your key go to
https://www.microsoft.com/en-us/soft...nload/windows7 and input your key to download an installation ISO.