Is your minidisk player part of a Hifi setup?
If so, it should have some rsa sockets for line out, you need a cable with 2 rsa plugs to go into these, the other end of this cable should have a 3.5mm stereo jack plug to connect to the line-in socket of your sound card.
If you have Nero there is a wave editor in that, or failing that download "Goldwave" from click here, this is shareware, but allows you almost unlimited access to recording as wav files.
The resultant files are around 30mb if recorded at CD quality(44khz). If you can get about 27 or so 3minute tracks this will give you enough to burn a CD using the "disc @ once" method.
If you want quality recordings keep your burn speed down to 8X or 16X max, otherwise you may get faults which will not be apparent until you playback; and it's too late then.
Hope this helps, and I'm sure you'll get more advice from the wizzkids on this furom,