That's a strange one. The only thing I can think of is to boot from a Mandriva live CD and see if you can choose a destination and restore your backup onto your new distro. I have no idea if it would work, it's a while since I used Mandriva properly so I can't remember it in great detail.
I suspect, the easiest option for you may be to re-install Mandriva, get that backup restored and then save manual backups of your files that are straight archives. Unless anyone else has a better idea, that would be my second choice in your situation.
From there you'd obviously still need to make a backup, but I'd suggest something like my manual method:
The way I do my distro hops is I have a partition with backup files in it - all my music and documents are there loose so I can access them without having to open archives. I keep them there as a backup and it means I don't *have* to copy files into each new distro I install. I then make a folder and call it say Mandriva, then I take any .folders I want to preserve and put them in that folder on that partition. So my browser, email, gimp, that sort of thing. Then I can pull the folders straight into my new home folder and that works fine.
If you need to compress some of your backup, I tend to do it by folder - so pictures in one, documents in another, that sort of thing.
The handy thing with my method is that all you need to do after your first backup is add any new or edited files to your backup. And make that .folder backup. I used to keep a wee checklist so I didn't forget any of my important .folders, but it's surprising how quick you can do it.
Hope you get your files sorted out.