can you hear the audio from the cassette through your computer? if so then you can record it with Windows Recorder, but you will have to stop and save the digital track after every song. You can probably get software to make it easier.
If the player has a line out you can patch to the line in on your audio card. You would need a RCA to 3.5mm plug for that. That's a common patch cable so you shouldn't have trouble finding one.
As for recording software I'd use Media Encoder 9 from Microsoft. It's very flexable and it's free.