Clock, Radio, and License Plate Light

After a hail storm my 2005 Chevy Aveo started having electrical issues. Every time I start the car or open the door the clock resets to 1:00. The AC buttons also reset (not the knobs, I mean like the AC button and the recirculation button). The radio also stopped working completely, no display or response whatsoever. The license plate light also stopped working, and I've changed the bulbs, so it's not that they're burnt out.
Another note: if I change the dome light to on or off the clock turns off completely. It only displays if the dome light is on Door.
These all started at the exact same time, so they are definitely all connected.
Any ideas?