Typically even if there is trickle power but the unit will not power on, only 1 LED lit on the logic board (the one for trickle), the power supply is typically at fault. If you have a spare power supply to test with you can boot the machine and look in the logs for "-110" . You will see, and a forget the exact wording, but something along the lines of "SMU Shutdown Cause -110". This is a clear indication of power supply failure.
In my experience the most common symptoms of logic board issues are, the obvious leaking and bulging capacitors, video corruption, and fans that constantly run at full blast even with lower CPU load. I have very rarely, if at all, worked on one of these that would not power on at all but no capacitor issues. However it doesn't mean it isn't possible.