1. Battery Charger - Possible, but may be ineffective and or dangerous. The power supply in computers are typically 350W supply. Ohm's law states Watts = Volts x Amps, thus working out to be 350w/120v = 2.9A. You can fiddle with the input voltage and go from 2.9 to 3.15, its a small difference. These power supplies are no designed or engineered to run at full power for a long time. This is also the power supply will not supply the 5v or 3.3v lines, unfortunately I do not know the max amp of each power supply line. Using this as a trickly charger may work, but you will be popping power supplies frequently.
2. Electrolytic cell - Again using the numbers in the first thought, there isnt enough amps for the electricity to cut through the plating.
3. DC to AC power - Yes they make them. The range from 100 watts up to 3000 watts if you want to get crazy. You can find them at Radio Shack, Wal-mart, truck stops, auto parts stores and nearly any retail place that has an automotive section. I have a 750 watt unit for camping and it powers my airbed, lights, music, and what ever else I need for the weekend.
Great visions to reuse the resources at hand, but they are not going to have the oomph you need.
Dennis