I have a Ford Probe with a similar setup.
If you can identify the wires, and get a matching connector then just wire the computer straight to the amp. If you can't lay your hands on a connector you could always cut the wires, but then there's no going back
It shouldn't matter that the inputs have common ground, just split the PC ground to each negative input.
I used the motherboard's onboard 4 channel sound, then found that most PC apps use only the front two channels for music... but it's good for films etc