[you posted in General]
Calibre does not have an 'Account'.
It is FREE (although donations will not be tossed back

)
Your Library
was stored on your OWN computer. If you made a full backup, you need to restore the Library Folder to the New computer
http://manual.calibre-ebook.com/faq.html#id41
What is not mentioned in the FAQ, is how to find that folder WITHOUT Calibre.
Search for metadata.db. The correct folder will HAVE FOLDERS for all your authors.. (if there are no author folders, you found an empty library...try another search result)