It can be done only if you use a power adapter to connect the old harddrive to.

Another way is to purchase an external harddrive enclosure for 20 dollars or so and install the old harddrive to it. Connect it up and transfer the data files (no programs or applications can be transferred. Once done then format the old drive and you have yourself an external storage.

edit....make sure the enclosure supports the connection of your harddrive as there is IEDE and SATA connections for the harddrives.