Once you have the hard drive out of the case, and considering its age, it will no doubt be an IDE or PATA type and not the more recent SATA type.
to be sure, just look at the connections to the hard drive itself, if a long strip of connector pins it will no doubt be IDE, if on the other hand the connections are in two or three separate blocks of connectors, mostly edge type, it will be SATA. It may also say somewhere on the label "SATA"
Ideally,if there are similar connections available on your main computers motherboard, a short connection lead is all that is required to connect directly to the motherboard and therefore the computer.
However, if for example your external drive is IDE, but the motherboard only supports SATA, then a USB adapter cable is what you require as being the only alternative.
Be aware though that if the actual hard drive itself has died, then even connecting it that way,will not give any results.
Edit to add pictures of hard drives, this first is a SATA type
This second is an older IDE type. You will need to know which type of drive it is to order a USB connector.
Edited by Plastic Nev, 17 August 2014 - 02:30 PM.