Yes, apparantly it is possible to hook up my 15 year old "boom box" to my computer via a headphone output --> mic input connector. Lucky, I happen to have such a connector lying around my apartment. The quality is far from spectacular, the levels are too high, but at least it's recording on my sound editting software and will soon be transferred to CD.
I'm sure those in need can buy the connector at radio shack or on the net.