Hyundai Tiburon AC radio lights out of commision

Ground wires go to ground; they can't be shorted besides. If a 12 volt feed wire were shorted, first of all that doesn't happen by momentarily connecting the cables backwards, and it would cause a fuse to blow. Did you check fuses under the hood and inside the car? The interior light circuit is often used for the radio's memory circuit for the station presets and clock. Most models will not turn on if that memory circuit is dead.

Do you have some really large fuses under the hood? Some in the range of 30 to 50 amps, and a larger one that's bolted in? If not, your car might still use fuse links which are wires built into the rest of the harness. Those wires are smaller in diameter so they are the weak link in the chain, and the insulation will not burn. They take a few seconds to burn open so hooking the jumper cables backwards for just a split second shouldn't have hurt them, but if you do have them, they are tested by pulling on them. If they act like a wire, they're good. If they act like a rubber band, they're bad. Typically they are bundled together and not covered with tape. They will be dull green, white, gray, orange, or black. The color denotes their current rating.

If you don't have fuse links, the next logical suspect would be the Body Computer. They run the interior lights but I've never seen one involved with the radio. In fact, your radio might have a red 10 amp fuse plugged in on the back of it.