You said you copied the library folder
as per the FAQ.
Again as per the FAQ, you need to copy the entire configuration folder from the old computer, and
replace the configuration folder on the new computer.
Both computers are running >XP, so that folder should be:
C:\Users\AlexBell\AppData\Roaming\calibre\
If in doubt, do as the manual says to locate the right folder.
Old computer:
C:\Users\AlexBell\AppData\Roaming\calibre\
copy to flashdrive
New computer:
C:\Users\AlexBell\AppData\Roaming\calibre\
delete this folder
copy the folder on the flashdrive to replace it.
...
If you've copied both the configuration folder and the library folder, you should end up with the exact same calibre setup. This works for many people, and I have every confidence it will work for you as well.