Here is a good tutorial on reinstalling grub2:
Just use the first method that is listed there. It should work fine.
To install grub2 to the MBR of your external hard drive, make sure you choose the correct drive. If you have 2 hard drives, one internal and one external, the external drive should be listed as /dev/sdb. You can confirm this by running: "sudo fdisk -l
" from the terminal on the live CD and choosing the external drive.