Hi,
As Brian said, could be beyond hard finding the cause without circuit schematic and so on. Anyway, where there's a will there's a way sometimes with a bit of luck: if a great part of the circuit isn't zapped, I'd forget buying another tester for now. You (may) need to discharge the capacitors somehow before fiddling with things, not sure how to do that, you'd need to find a suitable way.
What's the oil slick gunk on the back of the battery? Is it silicon/glue or something that shouldn't be there? Perhaps you could try starting with changing that capacitor, perhaps the cell battery (if it doesn't give - presumably - 3V on the voltmeter), maybe the crystal if it's got burn marks on the pins - but Brian said that is last one unlikely. If you turn it on and it dies quickly like it tries to work but can't that could be a short somewhere - I had a capacitor fail a few days ago on a breadboard driving me mad looking for the sudden odd circuit behaviour as I thought it was anything but a bypass capacitor.
You may just have to replace the whole board, to be honest with you as it may be very time-consuming locating the actual fault. Or if there was a short-circuit/surge of current - just how far into the circuit are things fried? I would have a go at least replacing the suspect capacitor though, if you really can't send off for an instant under guarantee replacement board.