I was finally able to successfully restore a backup. I began by first enabling booting from my CD drive, then inserting the first (and in my case, only) CD into the drive and turning on the computer. This caused the computer to boot into the DR-DOS OS BackItUp burns onto the CD to make it bootable (and presumably also the DVD).
The nrestore.exe program starts up automatically. As before, if the drive to be restored isn't already formatted, nrestore.exe can't do anything with it. So I tried exiting nrestore.exe without attempting to restore anything (use the arrow keys before selecting a source drive) and running DR-DOS's fdisk. With it I was able to create a primary partition in FAT-32 (choice 3) on the drive to be restored. FAT-32 was the newest, bestest filesystem choice DR-DOS's fdisk has.
After creating the partition, I executed nrestore.exe again, and this time it allowed me to restore to the newly created partition. I still had the same problem that although it said the restore was successful, I couldn't read anything on the drive. When I checked the drive properties in disc manager it was listed as a RAW drive with no filesystem identified.
I booted back into DR-DOS with the BackItUp recovery CD and noticed that from DR-DOS I could see folders and files (in 8.3 format) on the newly restored drive. This got me thinking that perhaps I could copy those files to another good drive on the machine using DR-DOS. But before I did that I decided to try a backup and restore of a FAT-32 drive (all my drives are NTFS, and that is what I had been working with up until this point).
After reformatting my test drive and putting some test data on it I backed up the drive with backitup and then deleted the partition. Now I was back to square one, except this time instead of trying to use the BackItUp recovery CD, I formatted the drive to be recovered with NTFS from Windows 2000. Then I booted into the BackItUp recovery CD and attempted the restore again.
I was able to restore, and this time when I rebooted I found that the restored drive was listed as an NTFS drive and the folders and files were recovered and accessible.
Apparently when I tried to restore the NTFS volume using the recovery CD's tools, nrestore created a hybrid volume that was half FAT-32, half NTFS, and readable by nothing except DR-DOS.
Anyway, if you haven't already tried this exact series of steps, I recommend that you do:
1. Wipe your system clean and install a fresh copy of Windows 2000.
2. Install, if you don't already have one, an empty drive onto which you will attempt recovery of your data.
3. Create one primary partition on that drive and format that partition with NTFS (I am assuming your original drive that you backed up was also formatted with NTFS since the symptoms seem to match that scenario).
4. Make your DVD drive bootable by editing your BIOS settings.
5. Put the backup DVD you made with BackItUp into the DVD and boot the system. Nrestore will start automatically after DR-DOS loads.
6. Restore to the empty drive you have prepared.
7. Boot back into Windows 2000 and see if the restored drive is visible.
8. Copy folders and files to where you really want them.
If this doesn't work, then try booting again with the BackItUp DVD, exit nrestore immediately, and see if the restored files are visible from DR-DOS and report back.
For best chances of success you might want to ensure that the disc to which you will restore your data is configured exactly the same as it was when you backed it up. This might mean, if the above steps don't work, that you have to prepare multiple partitions on it. For example, if the original drive had a 10 GByte partition in FAT-32 and a 20 GByte partition in NTFS, even if you only backed up and want to restore what was on the 20 GByte partition, you may need to prepare the restoration drive with both partitions in their respective sizes and formats prior to using nrestore.
Please let me know how it turns out.
P.S. By the way, I also found a bug in BackItUp at the creation end. One of the reasons I was having trouble earlier is that BackItUp reported that it successfully backed up my first test drive when in fact it did not. It only wrote the boot programs, the nrestore program, and an empty .dat file to the CD. Don't ask me why, and don't ask me why it considers that to be a "successful" backup.