|(edited) Forget about checking the voltage on the power switch connections.|
I hope you got a compatible power supply. Compare the color of the wires. They need to be very similar.
It could be a motherboard problem or something connected to the motherboard that is causing the problem. I would disconnect all the devices from the motherboard. Pull all the cards including the RAM, but not the CPU. When you power up, you should get some error beeps (if there is a speaker connected). Getting error beeps is good. That means the motherboard and CPU are working and something connected to the motherboard is probably defective.