Just to nail down the symptoms a little, it doesn't sound very good when you play Audacity, either, right? The export symptom is a red herring.
<<<the other end to the headphone jack of the laptop (note: there is also a microphone jack on my laptop but your instructions say not to use it, so I didn't)>>>
We tell people not to plug into the Microphone Input because Windows laptops tend to have
no places to plug your cable in. The Headphone socket is designed to send laptop sound to your headphones, not accept sound from somewhere else. The Microphone socket is designed to greatly amplify a special PC mono microphone. Most laptops have no place to inject a stereo music signal. They're business machines.
So you have the wrong computer. You need a machine with a Stereo, high level, Line-In socket. Deskside PCs have these (usually blue) and almost any Mac. Most Laptop PCs don't.
You can create a Line-In with your machine by use of an external USB soundcard.
http://forum.audacityteam.org/viewtopic.php?f=27&t=9477
Koz