Generally your PC will have a "line out" which is an un-amplified audio signal. So you need to amplify the signal to deliver some decent volume to drive the existing speakers.
This can be done a number of different ways.
Here are a few options:
1) Hack a set of amplified computer speakers. The wires that would normally attach to the satellite speakers would get wired into the existing cabinet speakers.
2) Use a dedicated home audio amplifier. This could be an old (or new) stereo receiver or a small dedicated amp (such as the one kevinp pointed out here:
http://forum.arcadecontrols.com/index.php?topic=79015.0)
3) Car stereo amp. These generally run on 12v which can be tapped from your computer's power supply. They are readily available and can be very inexpensive.
Good luck!