If attempting to program the unpowered microcontroller is what caused your problem, and it sounds like it is, replacing it will fix it (this is the only solution we know of once the chip becomes unprogrammable). Do you have the tools/experience to replace the ATmega168 yourself? If not, you can send it back to us to take a look at; just make sure we can identify who its from and where to return it. Before trying to replace it, I recommend seeing if you can talk to the 3pi at a lower ISP frequency. If so, you can fix the problem by resetting the fuses with a programmer running at this lower frequency.
It shouldn't be too difficult to keep this from happening to your students. All of our sample programs display the battery voltage at start-up, and you should encourage your students to add this feature to their programs as well. You can obtain the battery voltage in millivolts by using the read_battery_millivolts_3pi() function from the Pololu AVR library, and you can display the value it returns on the LCD using the print_long() function. If the battery voltage falls below 4.5V for NiMH cells, we strongly recommend you replace them with freshly charged batteries before you program! You could even program the 3pis to emit an annoying string of beeps once the battery voltage is too low.