"When I plug it in, the computer beeps and says 'Found New Hardware'"

Are you sure that's not the USB cable? I've never seen a PC that 'recognizes 1/8" Jack inputs like that before... For this process you don't NEED the USB cable at all...

1/8th" jack cable... male on both ends... one end goes into the Headphone jack on the MD recorder... the other end goes into the "Line In" on your PC soundcard (The one at the back...

"Nothing happens when I plug them together."
You may have to tweak your audio settings using the "speaker" icon in your system tray...