Welcome to TechIMO.
I would think the easiest way to do this w/o any hassle, is to just pull the hard drive out the old computer, look on the back (or bottom) of it for the jumpers, and set them to "slave".
Then just plug in the power and IDE cable from the new system to the drive, fire up the computer and copy the files you want.
When you have all the files you want, just switch the jumpers back and replace the drive.
Very simple. No software or hardware.