Tell ubuntu to ignore dead hard drive during booting?

Disable it in the BIOS?

Looks like there may be a way to tell udev to ignore it, though I don't have access to a system right now on which to test this.

As root, open up /etc/udev/rules.d/60-persistent-storage.rules with your favorite text editor.

A few lines down, you'll probably see a line that looks like this:

# skip rules for inappropriate block devices
KERNEL=="ram*|loop*|fd*|nbd*|gnbd*|dm-*|md*", GOTO="persistent_storage_end"

Add "sdb*" to that second line, so it looks like this:

KERNEL=="ram*|loop*|fd*|nbd*|gnbd*|dm-*|md*|sdb*", GOTO="persistent_storage_end"

Save the file and then reboot.