I have just experienced this issue as well. The way i solved this issue is to remove the motherboard from the console and re-flow the motherboard. By re-lowing i mean i put the motherboard into the oven for 15 minutes at 350*F , so yeah, the risk is real =)
The plastic that surrounds the av out, power, and controller ports, get warm but do not melt from the heat. sadly i cannot say the same for the plastic that holds the power button locked in place, can and will melt.
My PSone is working perfectly now. I wish you the best of luck with your repairs, hopefully this process will help you too.