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metadata.db
A normal Library will have lots of Author folders.
THAT ENTIRE FOLDER IS YOU LIBRARY.
Just copy the folder to its new home.

The folder name is the Library name. When I move it I changed the default name to 'Main' (pick a name).
All you need to do in Calibre is point it at whatever Library you want to use.
Create/Switch: Use EXISTING: <choose new home>
But before that, consider
replacing the configuration folder with the old one.
From a command prompt
Code:
cd %appdata%\Calibre
to see where it is on your new system. Should be in a similar location on the old drive