Possible Motherboard/CPU Failure on a Gigabyte K8 (GA-k8NS)

I am looking for some advice for a strange issue I am having with my PC. I work in the tech field but this issue has me a bit baffled and leaning towards a motherboard failure. Here is the issue:

The PC itself only turns on by the power switch in the back of the PC. You have to turn it on (using the switch near the power supply) and off 3-4 times for the PC to actually turn on. Once the PC is on there is no POST and no display on the screen. The only way to turn the PC off is to turn the switch off near the power supply. Holding in the power button won't actually do anything and it will keep running. Once the PC is on -- all of the fans are working. There are no beep codes but just a constant high pitched noise. The noise actually dies off slowly when you turn the power switch off (it doesn't instantly go away)

I replaced the power supply first with another known working power supply and it would do the same thing with a completely different power supply. I've also disconnected all drives/peripherals and all memory modules. Cleared the CMOS as well.

Any recommendations/advice as to what to try troubleshooting next would be appreciated   Thanks for your time.