You don't necessarily need any extra software. Your soundcard's mixer should have an option on the Record level slider to "record all" or something similar ("All" on some Sound Blaster types). Then any sound being made by/going through your 'pooter should get recorded. You also may want to mute any sound sources you don't want to record, like the CD player, the synth, etc. (so you don't get extra noise or Windows beeps and the like). Just have the Volume, Wave, and Record sliders un-muted. Hit record in the software of your choice, and start the playback.
Even if the site won't let you digitally copy/download the file, or blocks it in other ways, this should work (as far as I know). As far as I know, if it plays through the speakers, this method should capture it. Could be wrong, I haven't done this very often.
This method can also be used to record the audio your 'pooter plays when playing a MIDI file.