Hi Darren,

You might need remove to manually remove your thunderbird profile after uninstalling as @Zenos mentioned on this thread https://support.mozilla.org/en-US/questions/1162516 you can go to \Users\<you>\AppData\Roaming\ on Windows. On Mac, the profile is located at ~/Library/Thunderbird/Profiles which you can navigate to using Finder>Go>Go To Folder. Be sure to back up this file if you need it for offline folders, etc before you delete it.

I am wanting to add a new key for Open PGP on Thunderbird 78.9.0

The latest release version is 78.11.0. Before anything else, update to the latest version.

Nothing happens when I press the "New key" button.

If updating to the latest version doesn't help, try to start Thunderbird in safe mode. https://support.mozilla.org/kb/safe-mode-thunderbird

Is there any difference?

I have tried doing a re-install but that doesn't make any difference.

Profile files are stored separately from the Thunderbird program files. The program files are static and do not change (except when you upgrade the Thunderbird application version). Because we store profile and program files separately, you can uninstall Thunderbird without losing your messages and settings, and if something goes wrong with a Thunderbird update your information will still be available. It also means that you don't have to reinstall Thunderbird in order to delete your information or troubleshoot a problem. https://support.mozilla.org/kb/profiles-where-thunderbird-stores-user-data