OK. I don't like to have 2 boot partitions on a same system; for tests:
- boot from your Live CD
- open GParted: Applications > System Tools > GParted Partitions Editor (password is root)
- select /dev/sda1 device
- click on Partiton > Manage Flags
- uncheck boot flag and [Close]
After this, probably you won't be able to boot from sda but you'll just have to check the boot flag again
Now we are sure that you'll boot from hdb using /boot/grub/menu.lst from hdb1.
If on /dev/hdb1 your /boot/grub/menu.lst is like this:
# /boot/grub/menu.lst: GRUB boot loader configuration.
#
# By default, boot the first entry.
default 0
# Boot automatically after 8 secs.
timeout 8
# Graphical splash image.
splashimage=/boot/grub/splash.xpm.gz
# Change the colors.
#color yellow/brown light-green/black
# For booting SliTaz from : /dev/hdb1
#
title SliTaz GNU/Linux (cooking) (Kernel vmlinuz-2.6.37-slitaz)
root (hd0,0)
kernel /boot/vmlinuz-2.6.37-slitaz root=/dev/hdb1 quiet
it should boot in SliTaz now.
Eject the LiveCD, reboot and tell me what happens.