The circuit looks like a boost converter with IC9 as the controller, TR1 as a switching MOSFET, D1 as the diode. If TR1 failed (short) then it would not likely kill D1 also, so I'd suspect D1 failed first, which then caused TR1 to fail when it switched on (shorting C3/C4 directly to ground). TR1 is probably now open circuit D-S. The failure may or may not have been caused by a downstream component powered from the output voltage (over-current causing D1 to overheat and fail).
As a boost converter, the circuit input is likely 5 V (or whatever you can measure across C18, rated at 10 V). R18/R19 form a voltage divider which feeds into IC9, and if I'm correct R18 is marked 184 (180k) and R19 is 203 (20k), so the divider is 1:10. If the IC9 controller uses the familiar 1.2 V reference/feedback input then the regulator would be outputting 12 V when working. This also aligns with the 25 V voltage rating on the capacitors C3/C4.
You could try removing D1 and TR1. Then connect a floating, 12 V current-limited supply across C3 or C4. I'd start with current limit of 0.1 A, and I'd probably add some series resistance (10 to 50 ohm). Then you have a power limit of < 1.2 Watt, which may still heat a damaged (short) component on the 12 V rail, but is less likely to immediately cause damage. Apply this voltage after power on the system, not before. The boost converter doesn't look very big so I'd not expect it to deliver much current when working. If this works, and the current isn't excessive, you can try replacing D1 and TR1. D1 is likely a Schottky diode (cathode to R18) and TR1 an N-MOSFET, GDS on pins 123. Values are probably not critical on a small boost converter like this; use almost any device described in the datasheet as suitable for DC-DC switching regulators. Check R18/R19 (may need to remove them) since a failure in one of them could have caused the failure in the power devices. Instead of fixing the boost circuit, you could remove the TR1, D1, IC9, and connect a separate boost module across the output (C3/C4) to provide 12 V.