I got my radio back!
Apparently, it was a ring of punk kids fleecing the neighborhood. They got caught red-handed.
I hooked the radio back up to the car, (just plugged in the wire harness!) and it works, although the removable face was kinda jammed. I wiggled it around until it popped on and off cleanly again.
I still have to properly mount the radio. Maybe this time I put some gigantic bolt straight through the back of it into the car frame!
The only real downside to this incident is that I still have to return a new radio to Wal-Mart! Oh well, they have a pretty good return policy!