Assuming that the hard drives still work...
Follow this article to disassemble your device...http://buffalo.nas-central.org/wiki/Disassemble_the_LS_MINI
Attach both drives to the SATA interface of a computer that can access the internet.
Download and burn the Ubuntu 10.04 Desktop Edition CD-ROM from here...http://releases.ubuntu.com/lucid/ubuntu-10.04.1-desktop-i386.iso
Make sure the drives are attached to the primary and secondary SATA ports of the computer
(so Ubuntu will recognize the drives as /dev/sda and /dev/sdb).
Boot Ubuntu 10.04 Desktop Edition CD-ROM on computer.
Select language as desired (English).
Click on "Try Ubuntu 10.04 LTS" (to use Ubuntu without making any changes to your system).
Open a new terminal window (Applications | Accessories | Terminal ).
Start a new bash shell with root privileges...
Install the mdadm package (to administer RAID volumes)...
apt-get install mdadm
Attach RAID volume...
echo "y" | mdadm --create --verbose /dev/md1 --level=0 --raid-devices=2 /dev/sda2 /dev/sdb2
Mount RAID volume...
mkdir -p /mnt/lsmini
mount -t xfs /dev/md1 /mnt/lsmini
Copy files from /mnt/lsmini to your backup drive
Once you have completed the backup, try to unbrick your device by reverting to stock firmware...http://buffalo.nas-central.org/wiki/Revert_Buffalo_Linkstation_Mini_To_Stock_Firmware