This is where you start: First, clean all the wires with "carb and choke" cleaner on a rag. Clean everything! Next, unplug the battery and don't touch it till your done... Next, take the tape off of all the connections and remove the stereo, junker. Look at each individual cut wire and figure out where the other end is and solder them back together while using shrink wrap to cover the exposed wire that you just soldered. When every cut wire looks like it is together with its other half, place the battery wire back on. Try out your lights, and all the other stuff that didn't work. Then go from there. I would highly recommend a wire schematic for your year vehicle. Then trace all the wires to see were they go. Even the unplugged ones in the engine bay.
Been there, done that.