I did a google search and found www.installdr.com with wiring diagrams for all sorts of cars, including mine. Indeed the correct wires are plugged into the correct places now. Ignition is going to ignition, battery is going to battery, ground is going to ground (the only wires that my car has) and the fuse is good after having been replaced.

The Empeg comes on and stays on permanently, the Rio Car comes on and when it finishes booting up, powers itself off. The amp also apparently stays on permanently, as I can hear my Empeg with the keys out of the ignition.

Obviously the best solution is to just buy a new car.