Take the drive out of the old computer. Then get on eBay and buy an external drive mount (they are cheap <$50) They are USB ports so you can open the individual directories from another computer. I use a couple from BlackX thermaltake. They will accespt both the tiny laptop drives as well as the std size drives. No special mounting just drop them in. They make great backup units as you simply buy plain drives and store them.
note: I have saved several drives from 'dead' computers and salvaged the directories and files from them.