Check the diode bridge with the IGBY out and the AC disconnected, it should be detectable as 4 diodes. If one is shorted it will show. This is most likely a transfer switch, and probably was destroyed by a short across the output, which killed the IGBT. It is designed to apply the AC from the mains to the output, and to disconnect the inverter from feeding back into the mains.
Check the relays have not got shorted contacts as well, and try running it with the IGBT out, which will tell you if the bridge is breaking down with voltage. The diode, resistor and capacitor are a snubber across the IGBT, to keep spikes from damaging it.