I found that you have to export from Calibre on the old computer and then import that into Calibre on the new computer. See here:
<http://manual.calibre-ebook.com/faq.html#how-do-i-move-my-calibre-data-from-one-computer-to-another>
http://manual.calibre-ebook.com/faq....ter-to-another
And just know, anyone who is trying to do same: from what I've read everywhere, stay working within Calibre when you change, move, delete things.
I mean: don't go outside of the program, move files, delete files, etc. Just messes you up.
So, don't try to go into your Windows Explorer (or wherever) and copy or move files (like I mistakenly did a few times). Instead, use the Export feature inside Calibre and the Import feature after. (And don't do as I have done, delete books outside the program.) Make the program work for you and it is easier all the way around. AND DO NOT USE 'add books'... that is for books themselves that you want to bring in... When moving a library, you want to bring in all the stuff you've setup prior...like all the metadata, etc. So, avoid Add Books when moving a collection/library. What you really want to move is the database itself and using Import and pointing Calibre to yours is the way to do. Good luck. Keep it simple. Read the Help link above.