This is not, obviously your UPS (since it's the whole UPS, not just the charger circuit), , but it's a start:
NOTE! Lethal voltages present. Take all necessary precautions.
With NO POWER applied to the board(s), I would start by
carefully wiping off the tops of the ICs and the transformer (which seems to have a circuit displayed on it) on the board you showed in post #10. Let us know whatever numbers that are displayed, as this will help with the troubleshooting. I'm approaching this from the assumption that one or more of the solid state devices (bridge diodes, opto-coupler or IC chip) was fried by the surge. Could, of course, be something else, but got to start somewhere...
With the board powered up, confirm absence/presence of AC voltage (and what that value is) at the output of the transformer. Then confirm that AC level is at the appropriate diode junctions of the bridge (presumably those 4 diodes closest to the transformer - check the traces under the board for connections to the transformer). If present, check the other two junctions for a DC level and its value.
If no DC, replace all diodes. Note that they may blow again at power up due to some downstream problem, but diodes are cheap.
If DC is present, stop, power down and we'll continue with the troubleshooting.