If you still have your old computer (and it works) You can just copy the Old Library Folder(s) to the New one.
If it is broken,
BUT the drive is still good. Remove the drive and:
mount in a USB caddy / use a USB clone adapter (drive is run bare) / Mount as an extra drive in a Desktop system
Then select that Library (Switch/Create: use existing)
AND
immediately take care of the no backup problem
Select All Books (ctrl-a): right-click Copy to Library: <the Main one>
depending on how many, this could be minutes or many hours (thousands of books)