Using Knoppix, if you do
# fdisk /dev/hda
followed by 'p', you should see two partitions: a small one at /dev/hda1 and a larger one at /dev/hda2. Both should have a partition id of 'fd' indicating a Linux RAID partition. Your data files are on the larger one /dev/hda2.
If you use the 't' option on fdisk and select that partition and change its type to '83' it will become a standard ext3 partition.
You can then use fsck to try to repair the partition before getting your data off -- or you can simply mount the partition and try to copy your data to another drive. (Others may have opinions about what is best.)
Search the forum or check the manual to see which directories are included in backups and these are the ones you should try to backup. Unfortunately, since you were unable to do a pre-backup event, your mysql database may not get restored correctly when you put the data back on a fresh install.
Hope this helps. Good luck.
John