Sounds like the transistor's your best option to fix it. I think it signals the PSU to turn on and without the collector held at 3.26 to 3.3Vdc the PSU won't come on.
If you have a multimeter, you could check the voltage level at the transistor's collector (RED multimeter lead) with respect to GND (BLACK multimeter lead to case shield or one of the screws that hold the motherboard in place.).
How To Test a 1.6 Psu
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Test with the console plugged in or unplugged?