Actually I do have this data backed up. I did not know that when one reinstalled Windows that one needed to disconnect the drive.
It's definitely NOT MANDATORY. Windows will install perfectly fine to the target drive/partition of your choosing, as long as you control the installer properly and your BIOS boot sequence is set properly with the multiple drives still connected, etc., even if you have multiple other drives still present and connected.
Disconnecting your "data" drives is simply super-conservative and guaranteed protective good technique, which of course would guarantee you couldn't make a mistake by accident and destroy something you had no interest in destroying. And as has been mentioned, this approach also guarantees that your "system reserved" partition (which is marked "active" by the installer, and is where Boot Manager is placed) will be on the same drive as the true installed Windows system partition itself.
Note that this is obviously inappropriate if you just added a second drive and want to place the new Windows to be installed on this second drive, when an existing bootable OS is already on your first drive. That would require the Boot Manager menu (in "system reserved" on the first drive) to be updated to point to your new second Windows on the second drive, something which would be done automatically by the Windows installer during this second Windows install. So disconnecting the primary drive in this scenario is clearly NOT what you want to do, because of the unusual target configuration you want to end up with in this very special case.
But for almost all normal one-OS installs, it is just recommended technique with good justification to "protect" any data drives from accidental unwanted damage during the current Windows install.
Thanks for the quick reply. I'll just have to move the data from my backup.
You could also first try Partition Wizard's "partition recovery" feature, before restoring from your backup.
If these drives have truly not been wiped somehow, so that the old partition contents on these drives are still as they were, PW may be able to discover the partition boundaries and reinstate them. You wouldn't have to restore them from your backup if so.
Worst case, if PW can't recover the partitions then you can still proceed with your restore from backups. Can't hurt to at least try using PW first, as it might save you a fair bit of recovery time that would otherwise be unnecessary.