I installed VirtualBox from the Ubuntu Software Centre on my new computer. I had already copied over my VM -- it came with all the other files when I copied everything under /home.
When I figured out how to run VirtualBox under Unity (it's under Accessories), it came up and knew about all the VMs I had on the old machine. When I started my Windows VM, it complained that it couldn't find "/usr/share/virtualbox/VBoxGuestAdditions.iso". Sure enough, the iso wasn't anywhere on the new machine.
However, for my purposes I didn't need the iso. I just unloaded the iso from the virtual CD device for the virtual machine, and tried restarting. It worked.
I would need the guest additions iso sometime, so, with the virtual machine running, I went to the Devices-> Install Guest Additions menu. It asked me if I wanted to download the file from the Internet, and I said "yes".