I've got a test program that blinks an LED on three Arduino Minis, over an I2C bus made out of FabricKit ribbon, in response to a signal from the LilyPad. Not shown is that I have a power cable that connects to all devices and provides 4.5V from a 3-cell AA battery pack. The system is now self-contained.
One snag is that I2C doesn't work unless three devices are connected, presumably due to termination issues on the bus. Longer-term I'll probably need to put some termination resistors on the unused I2C ribbons.
I also need to label wires and polarity before I sic this on students.