Been there, done that. This is quite simple. He had a PC that was broken, so he won't push to get out of the labor costs *if* he gets a PC that is fixed. Build or buy a PC that is as power as what he had (and if it is 3 years old, he'll probably be getting a better PC anyways) and he gets that for free, but you charge him for the original labor, after all that *was* done.
File an insurance claim with the shipping company you used, and get the original failed PC back, format it, and use as many parts that are still good as possible to recoup your costs.
In short, the customer did nothing wrong here so I'd be right there with him that he shouldn't have to pay for the labor of repairing a PC *and* a new PC. this is a "make it right" scenario, so ...make it right.