So it could be a multitude of things. I'll try to help though.
Just some clarification, when you "Discharge" by holding down the power button without power, it does discharge the capacitors, but you can press the power button 4-5 times and it solves that the same way. An easy way to tell if it is discharged is, if you look at the cpu fan and the power is removed, if there is power left in the system you can see the fan try and spin when you press the power button. Once there is no movement then it is purged.
The first thing I would check is the connections.
1) check the connection from the power button to the headers on the motherboard. They can become loose over time through movement. This is sometimes the cause.
2) Make sure your ram is seated correctly and hasnt become loose. (remember to try to power on and cycle after every change to trial)
3) If you have multiple sticks of ram, try removing one to see if you have a bad stick (Ive had bad ram and it will cause problems like youre having)
4) Try removing graphics card/reseating it.
5) If you have a spare power supply, try a different one in case that is the issue.
If none of these help then it could be a trace in the motherboard or chipset that went bad on the motherboard.
ps sometimes depending on the motherboard there is a button on it itself that you can use to power on and post to see if it is in fact the power button that is faulty.