You want to avoid a full re-import at all costs - you'll lose all your keywords, develop settings, etc. I did it by mistake once, not a happy chappy!
As you'll have seen by now, when Lightroom does a backup it only takes a copy of the database (.lrcat file) which contains all the keywords, links to images, etc. The image previews aren't backed up as they can be regenerated from the source files (the previews are just the source file with your develop settings applied). Indeed, my preview folder is ~50GB, so you can understand why you wouldn't want that being continually backed up!
When you say you "imported the backup catalog" do you mean that you opened LR with a new catalog and then imported the backed-up catalog? If so, that's not the way to do it (at least, that's not how I do it). The easiest thing is to literally copy the backup catalog in Windows Explorer, and paste it where you used to have your old catalog. Use "copy" rather than "cut" so that the backup is still there if you have further problems.
If you haven't moved your image files, then when you open the catalog you'll be back to where you were pre-drive failure (well, you'll be missing any changes between your last backup and the failure obviously).
However, you said you moved the image files onto C - you don't need to do this. Indeed, if you do, the catalog in LR still thinks they live where you moved them from (D:\My Pictures or wherever). So you need to put them back there and LR will find them again without you needing to do anything else. You could use a combination of Update Folder/Find Missing Folder to get them back, but it's easier (esp if you were happy with the location previously) to put them back where Lightroom was expecting them.
Once LR has found the images (no "?" next to folder) then it will rebuild the previews - it will do this itself as required, or you can go to the Library menu, then Previews and select the "Rebuild..." option you want to make it do them all in one go (means it will be quicker when using LR as it doesn't need to do them "on the fly").
Hope that helps.