I had even updated the drive letter and the volume name on the new drive, but Win 7 could not find any backups on the new drive after the manual copy. So Win 7 wants something it cannot find, but is not specific about what it wants.
I personally recommend you very seriously consider either deleting/moving unnecessary content elsewhere (perhaps to your USB drive), adding a hard drive to your computer and using that or completely replacing your hard drive and migrating your data over.
For best practice, the swap partition should be activated as swap once the USB drive/flash is mounted. Additionally, it's best to deactivate swap partitions before unmounting them.
Losing the swap file is actually a little bit more important than you think. If you're worried about free space, there are other things you can do, like disabling Hibernation for example.
Whether you're unable to boot into Windows or just want to learn new ways to manage files, you can use the Command Prompt to copy data from your hard drive to your flash drive.