At one stage I thought it was all relative to calibre-portable.exe's location, but someone convinced that was not the case - no names, no pack drill
So, maybe the problem is that the calibre portable installation went to say -
C:\My Portables\Calibre Portable, so calibre-portable.exe sets up the 'environment' around that path, e.g. it expects the config directory location to "C:\My Portables\Calibre Portable\Calibre Settings" and the library folders are expected to be at "C:\My Portables\Calibre Portable\" etc.
But Kythe42's backup (via Synchtoy) has copied
C:\My Portables\Calibre Portable to lets say
H:\Backup\My Portables\Calibre Portable but calibre-portable.exe maybe assuming the environment for the original location.
I do something similar, my libraries are at D:\Calibre\Libraries\, but on my backup drive (maintained by Goodsync which is similar to Synctoy, FFS etc) they're at H:\#DataBackup\Calibre\Libraries - I occasionally access the libraries on the backup drive with no problems, but via installed calibre not a copy of a calibre portable install.
@
Kythe42 - a simple cookbook solution isn't coming to front of mind. Basically you need to install a fresh portable onto the WD drive (NewPort), and then copy the library(ies) from the backup location (CalPort) to NewPort, what I'm not sure of is copying Calibre Settings from CalPort to NewPort.
BR