If you want to make a one time copy of your library from one machine to another, you need to do a little extra work. You've already copied the folders with the media files. I hope you copied them "as is" without rearranging anything. You probably did.
You also make a database backup on the source machine and restored it to the destination machine. Good! Now you need to do some extra stuff on the destination machine:
1. Start with a totally empty library. Do NOT set up auto import yet. If you let MC import files at this point, you'll get duplicates. Hey, you've seen that haven't you?
2. Restore your library (the database backup you made) and see that all of the files have little red minuses ( - ) next to them. This indicates that MC can't find them on disk, because their paths are wrong. Either the drive or part of the path is different on the Destination machine from how it was on the Source machine.
3. Let's fix that with the Rename, Move, and Copy tool. We want to use this in "Update Database" mode. This changes the paths inside of MC, but it doesn't try to actually move or rename files on disk. Which is exactly what we want! In particular, you're going to want to use the "find and replace" section of the RM&C tool. It's documented quite well here:
http://wiki.jriver.com/index.php/Find_%26_Replace_TemplateTry doing this on a small group of files first. Make sure the preview looks right. Then, after you press OK to change the paths, go look at those files and try to play them. If they work, then you did it correctly. Go do the rest. If not, you should start again. But let's hope you get it right the first time.
Good luck.
Brian.