Here's what I wanted out of this project:
Reasonable battery capacity, ability to recharge itself, reasonable audio fidelity, rugged durability, ability to charge/ power other devices [music players, phones, raft inflaters].
As far as I know, so long as I don't let the battery go flat for too long this box should be able to provide electricity and music for years without ever plugging it into the grid.
Step 1: The Box
Other options I considered were Pelican cases, tool boxes, and suitcases.