All the circuitry downstream of the power supply is the same for 240V as for 120V versions, so you won't have to hunt down a special flyback (if that turns out to be the problem).

I'm still a bit concerned about the capacitors. They're well sealed and designed to take full line voltage (and then some), so leakage from the battery should not have caused them to blow up. A serious overvoltage may have killed the caps, which bodes ill for the fate of many other components. Check the usual suspects you can (all semiconductors in the power supply, electrolytic caps). And if you happen to own an oscilloscope, drop a probe onto the 5V and 12V supply lines. The waveform you see (both in general shape and specific voltage swing) would be highly revealing.