The drive is certainly formatted. Don't know what you mean by "quick format", but probably if it used to be a Windows drive, it's filesystem was either NTFS (probably, if XP) or FAT (less probably). Neither of these work for a Linux install (except that mini-Slackware, but it's another case), so when you installed Ubuntu, it formatted the drive - if it was that drive you checked out - probably to ext3 (a journalling Linux filesystem). It may well have changed the partitioning also. It is
possible that it just resized the existing Windows partition on that disk and created a new one at it's side, but it depends on what you selected during the setup (it asks you whether or not you'd like to overwrite everything, resize or partition manually - what did you pick up?)
So, it looks bad. If it resized the partition, it's still there, intact (in case there was enough space). Probably, though, it simply overwrote the Windows partition (or were there several?), and in that case data recovery could be difficult if not impossible - the data is already overwritten, at least partly, so your only options are data recovery programs that can get data out of a newly formatted partitions, or use professional services that do this kind of jobs. They use some software too, but usually something you can't download from the web freely (or even with some cost).
If it was important, you'll want to pay for a professional to try. It is expensive, but so might your data be. If it is not important, just live with the fact; you said there were backups, so if your Windows installation is still all right, you can just re-backup (and do it quickly).
EDIT: a harddisk is not a good place to store backups in. Use a removable media instead, like tapes that can store several dozens to hundreds of gigabytes, and store them to a place other than where the computer is. And have several backups. A backup is useless, if it's in the same place where the computer is and could get destroyed at the same time, or if there's only one backup that could easily get corrupted. Back your backups too