Problem restoring files in Windows Backup

The hard drive failed on my friend's Win 7 laptop. I replaced the hard drive, now I am in the process of recovering documents that he had backed up on an external hard drive. He was using Windows Backup.
When I start the application in restore mode and direct it to the external hard drive, it shows a backup done on Jan 2. But when I browse through the backup folders using Windows Backup, it does not show any of his recent files. I went ahead and restored the folders, but the most recent files in the restored user folders are only from mid November. Any ideas what I might to do the see if the missing files were in fact backed up, or where they might be?
Thanks

Thanks, Brink. That was helpful in that it allowed us to see what was backed up. Unfortunately, for some reason there is lots of backed up data in AppData and some other system folders, but the user folders only appear in one of the zip files, and there is only 1 file in there. It appears that either the backup malfunctioned or was interrupted somehow. Unless there could be another reason why we are not seeing the user folders. Thanks

That is the only backup folder on the external hard drive.

Thanks

That's what it seems like. Have you heard of failures like this before, or is this a rare case? Thanks

I've tried quite a bit with the old disk. It spins, but is not recognized either in the computer or in an enclosure. I've tried about about 6 differents utilities - hirons boot disk, several utilities from the Falcon 4 disk, Partition Wizard recovery function. Also tried the freezer trick. I'm open to ideas if anyone has any.
I've not tried Recuva, but that requires that an OS can see the disk first, doesn't it?