I have moved over to a new laptop and installed my Acrobat Standard 9 version.
Different to before, now it is asking me when I open the installation to provide it with a serial key for an older version where this would be only an upgrade on.
Of course I didn't have that and wasn't asked before.
What can I do to use my version again?
First of all, Acrobat 9 is not compatible with Windows 10, so problems are to be expected.
You need to find out what kind of license you have. If your license is an upgrade then you can't install it without the serial number of a full previous version.