Flux Capacitor Box
I started by identifying the electrical box that was used for the real Flux Capacitor. Several web site seem to agree that it is a still available Stahlin Electrical box model J1210HPL. That means it is a Fiberglass 12 in. x 10 in. box.
I located one on eBay (where else) for about $70. It's not the correct color and needs a window cut in it, but it's the right one. It's also the perfect starting point. Here's a link to help you find the Stahlin Box.
Just be careful with eBay searches. If there are no Model J1210HPL Stahlin boxes available, eBay will show you other models. They will not work and are the wrong size or may not include the hinges and locking clasp.