Presumably you copied the serial number from the Help > About screen inside the software. That number is intentionally truncated by 4 characters.
If you are the owner of the serial number, you can retrieve the number from your Adobe account,
Failing that, try using Belarc on the old Windows 7 computer to retrieve the serial number.
Thanks. Running Belarc Advisor on my system retrieved the Serial Number for me and saved me time, i had already several hours on forums already.