I don't understand why you think you have to reinstall Linux (or Windows, for that matter). You seem to have had the bad luck that the power loss in the middle of the upgrade made your Linux installation unusable (or at least not easily usable), but that doesn't mean it's not recoverable.
The easiest way to recover would be to boot from a live CD or USB disk (preferably from Ubuntu 10.04, though any recent enough Linux should work). (It's probably possible to repair your installation by booting it in a particular way, but the live CD approach is a little easier.) The following commands assume you have a shell (command line) running as root (administrator).
If you have an interface that offers to mount your existing Linux installation, do what it tells you. Otherwise, do it manually: use
fdisk -l to see what partitions you have and locate the system partition. Mount it to some place. Also mount procfs and sysfs under it. For example, if your Linux partition is on
mount /dev/sda99 /media/linux
mount -t proc proc /media/linux/proc
mount -t sysfs sysfs /media/linux/sys
Start a “subsession” in the Linux installation with chroot:
You should now have a shell in your Linux installation. Run
apt-get install or
dpkg --configure -a to continue the upgrade. (Sometimes running these commands a few times can get rid of errors, or at least let a lot of things progress even if a few packages are blocked by an error.) It's possible that the crash left the system in a state where those commands aren't enough; if so, ask again, reporting the error messages you see.
Note that I do not recommend accessing your Linux partition from Windows if the purpose is to extract important data. Windows tools for Linux filesystem access are not fully reliable, especially if the filesystem was not unmounted cleanly.