Just to be clear, when you force the PSU's ON/OFF line to ON, is the backlight on and the video signal displayed fine?
I suggest rather than shorting it, cut the wire linking ON/OFF between the logic & PSU boards, then attach a 1k resistor from +5V to ON/OFF on the PSU side.
With ON/OFF connected again, you could try different input ports on the monitor to see if none of them make the logic board turn the backlight on.
You may be aware but be very careful testing the circuit as it has lethal 400V DC in the PSU and half of the PSU board is non-isolated (live). This is even the case when it is in standby. Luckily looks like your problem is not in the live circuit. Best keep the PSU PCB mounted in the chassis if at all possible.