Whip out your multimeter and take some voltage readings between various wires and ground.
You should have a constant power 12V for the clock/memory, and a 12V on with accessory/ignition for the main 12V stereo power.
Ground, you can check resistance to a (any) chassis ground point.
You could instead find the factory wiring diagram and compare to where the wires went on the old stereo.
Is the factory wiring intact still or hacked up? If intact, you might check major stereo brands for an adapter harness. Even if your brand of stereo is not supported, you can hack up the adapter harness to your new stereo wiring to leave the vehicle wiring intact, then just plug the intact vehicle wiring connection into that adapter harness.
If this diagram is correct it might help:
More here:
https://www.justanswer.com/car/0a2x4-2004-saturn-ion-quad-coupe-installing-new-stereo.html