While I am fairly new at this game, I am a computer technician by trade. I can tell you that VF is installed in the Windows Program Files, that means it is written to the registry and can only be removed through the Add/Remove Programs in the Control Panel or through a program uninstall which will remove it from the registry. Simply copying the entire game to the new computer will not work unless you first re-install the basic game on the new computer so it writes to the registry. You can then copy your old game family files to the new computer.
First backup all your LDW folder files on your old computer to a removeable media, such as to a disk or thumb drive. Also copy any image files you might have changed through the addition of any mods. Once the basic game is freshly installed on the new computer, you can then copy your family files from the old computer to the newly installed game program on the new computer so you don't lose your family.
As far as trying to copy and use backup files, you cannot overwrite a file if that file is currently in use by the computer. With only one family, the only way to do that is to close the game down, then copy and paste your backup file to the LDW\Virtual Families folder. An easier way is to create a second family, then pause the second family so you don't have to deal with it. You will then be able copy and paste your backup files for your first family by switching to this second family through the menu, the second family will remain on pause.
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WARNING: I cannot be held responsible for the above as apparently my cat has learned how to type.