Firstly, it isn't just a case of pressing 'CD' on the head unit and the head unit then producing output from the CD input. Two of the pins on the CD connector are for the Alpine M-bus protocol, which the head unit and the CD changer use to talk to one another. If the head unit doesn't get anything sensible over this bus, it will assume that there isn't a CD changer connected. See http://joerg.hohensohn.bei.t-online.de/mbus/ for some info on the M-bus protocol.

The head unit uses a line input to the best of my knowledge. Surely you can get line level output from a PC anyway so it isn't worth risking an amplified input.

Cutting the existing cable is the best bet, the CD socket on the back of the stereo is an unusual one (a Hosiden TCS6185, I believe) and difficult to find a plug for.

I found a pin-out of the CD socket on the web ages ago but can't find it now. I have a printout though, so here goes:
Top row, from left: right channel, signal ground, left channel
Middle row: ignition, power ground, not connected
Bottom row: M-bus ground, M-bus signal

Apparently Blitzsafe sell a product that provides a line input and gets around the problem of the M-bus by pretending to be a CD changer. Someone on Volvospeed is also producing a similar device, and is also intercepting the M-bus signals to pass to the PC over the serial port so you could avoid having a separate keypad and instead control everything from the head unit.

I haven't tried doing such a thing myself. I thought about it but figured that waiting for the PC to boot up would be frustrating and the hard disc would probably suffer head crashes every couple of miles.

Hope this helps,

FiveAlive