2007 Camry: Engine is non-responsive, Battery works okay

I was installing a dash cam while my car's battery
was on (engine was not running). When I was
pulling back some off the seams/weatherstrips
above the windshield to hide the camera's charging
cable, my radio and clock suddenly died. I thought
the battery might have died, but when I turn my key,
my lights and indicators work. The engine doesn't
make any noise though.