If both hard disks have Ubuntu 10.04, then I don't think there's any point in running a virtual machine. Why not just use
chroot? If sdb is mounted to
/media/olddrive, then you can run:-
$ sudo chroot /media/olddrive
Quite often though, you'll need access to all the system device folders in
/sys. In which case, you can use
mount to create them:-
$ sudo mount -t devtmpfs none /media/olddrive/dev
$ sudo mount -t devpts none /media/olddrive/dev/pts
$ sudo mount -t proc none /media/olddrive/proc
$ sudo mount -t sysfs none /media/olddrive/sys
Of course you can boot from raw hard disks though, with VirtualBox...
It should come with a tool
VBoxManage, which can create a ".vmdk" file that is basically a shortcut to the root of a hard drive partition. See here for a little guide on doing this. Note, this latter method isn't really recommended, but I've used it a few times and haven't had any problems with it. One gotcha is that you might have to run VirtualBox with extended (e.g. sudo) privileges to access the raw hard drive partition.