Here is a possible solution.

Three self powered oscillators in each switch (think small watch battery + 2 transistor multivibrator), each on a different frequency inductively coupled to the loop formed by their secondaries, and the secondaries of the three "leds".

The three leds are tuned circuits (think simple crystal set with the diode in this case being a genuine LED) inductively coupled to the loop, to pick up the frequencies being propagated round it by the three oscillators.

The battery is genuine enough, but it does nothing, since the battery snap is insulated, and has the red and black wires joined together, to complete the loop.

It might require some carefully hand wound inductors, or possible off the shelf smd rf transformers.

Simple, entirely AC, and very clever.

Here is a possible solution to the series puzzle.

Three self powered oscillators, one in each switch (think small watch battery + 2 transistor multivibrator), each on a different frequency inductively coupled to the loop formed by their secondaries, and the secondaries of the three "leds".

The three leds are tuned circuits (think simple crystal set with the diode in this case being a genuine LED) inductively coupled to the loop, to pick up the frequencies being propagated round it by the three oscillators.

The battery is genuine enough, but it does nothing, since the battery snap is insulated, and has the red and black wires joined together, to complete the loop.

It might require some carefully hand wound inductors, or possibly off the shelf smd rf transformers. (Like these for example http://www.entheo-electronics.co.uk/components.php )

In short, six transformer secondaries in a loop, 3 to allow signals to be injected, one by each "switch" and three to allow each signal to be received, one by each tuned "LED".

Simple, entirely AC, and very clever.

The same idea works for the parallel version, just requiring slightly different values and leaving the battery snap open circuit.