Okay this has been slightly trickier than I thought it would be; partly because of the problems I've had before with drives. I'm putting up the full process I've used because there's another issue I had (error 0x810000E3 when opening the backup) that seemingly other people have (three separate links) had but without any solution.
In short, to recover a Windows 7 backup (non-system image) you will need to restore:
The file /MediaID.bin in the root of the backup drive
The entire contents of \WindowsImageBackup
The entire contents of \[ComputerName]
It's also possible you might need a couple of Guid-named files and the contents of SPP in the System volume Information folder - I did do this because of some issues I was having but they didn't go away afterwards so only do this as a last resort; because you have to modify the permissions of that folder on your target drive, and Windows doesn't always take kindly to that.
You restore all of these into the root of another drive, then windows backup and restore should automatically find the backup. If it doesn't, then you should be able to search for it.
There might be issues if the current machine name doesn't match the original machine name and if the backup drive letter is not the same as it was originally - although most of these kinds of issues appear to have been related to Windows Vista; Windows 7 I think is more forgiving.
Then the last problem I had... and this will be particularly relevant if you're recovering a backup from a drive that had filesystem corruption or bad sectors.
When double-clicking the backup to open it I got an error like this:
There is a problem with the backup catalog. Restore from different backup or create new, full backup. (0x810000E3)
I ran ProcMon and narrowed the list down to the backup process (can't remember the exe now - but it was obvious as it was the one opening and reading .wbcat and .wbverify files). With it running I tried to open the backup again.
I noticed that it was getting to a particular .wbcat (e.g. Backup Files 190.wbcat) file and not reading it all the way through to the end like it had done with all the others. So I tried re-recovering it (I had had some issues with memory timings which I'd subsequently fixed) but still the same problem.
Clearly these catalogues were either corrupt, or the drive I copied them to is corrupt.
In the end I just deleted the catalogue file because the associated zip (in the parent folder) only contained some music that I can afford to lose (have all my music at work anyway). I had to do this a few more times, and in the end I was able to get Windows 7 to show me the contents of the backup and then restore it. I then did have issues with one file in the backup being corrupt (not ones I'd removed the wbcats for) - but backup and restore lets you skip those.
Of course, if you have to delete a lot of catalogue files then you're deleting parts of the backup and I can't say what'll then happen if those catalogues are from the differential part of it (mine were from the initial backup seed) - but it's about your only choice if you get this error 0x810000E3.
